{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
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    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Inferring parameters of SDEs using a Euler-Maruyama scheme\n",
    "\n",
    "_This notebook is derived from a presentation prepared for the Theoretical Neuroscience Group, Institute of Systems Neuroscience at Aix-Marseile University._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import pymc3 as pm\n",
    "import theano.tensor as tt \n",
    "import scipy\n",
    "from pymc3.distributions.timeseries import EulerMaruyama"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "nbpresent": {
     "id": "2325c7f9-37bd-4a65-aade-86bee1bff5e3"
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Toy model 1\n",
    "\n",
    "Here's a scalar linear SDE in symbolic form\n",
    "\n",
    "$ dX_t = \\lambda X_t + \\sigma^2 dW_t $\n",
    "\n",
    "discretized with the Euler-Maruyama scheme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# parameters\n",
    "λ = -0.78\n",
    "σ2 = 5e-3\n",
    "N = 200\n",
    "dt = 1e-1\n",
    "\n",
    "# time series\n",
    "x = 0.1\n",
    "x_t = []\n",
    "\n",
    "# simulate\n",
    "for i in range(N):\n",
    "    x += dt * λ * x + sqrt(dt) * σ2 * randn()\n",
    "    x_t.append(x)\n",
    "    \n",
    "x_t = array(x_t)\n",
    "\n",
    "# z_t noisy observation\n",
    "z_t = x_t + randn(x_t.size) * 5e-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "button": false,
    "nbpresent": {
     "id": "0994bfef-45dc-48da-b6bf-c7b38d62bf11"
    },
    "new_sheet": false,
    "run_control": {
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    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(10, 3))\n",
    "subplot(121)\n",
    "plot(x_t[:30], 'k', label='$x(t)$', alpha=0.5), plot(z_t[:30], 'r', label='$z(t)$', alpha=0.5)\n",
    "title('Transient'), legend()\n",
    "subplot(122)\n",
    "plot(x_t[30:], 'k', label='$x(t)$', alpha=0.5), plot(z_t[30:], 'r', label='$z(t)$', alpha=0.5)\n",
    "title('All time');\n",
    "tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "What is the inference we want to make? Since we've made a noisy observation of the generated time series, we need to estimate both $x(t)$ and $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "First, we rewrite our SDE as a function returning a tuple of the drift and diffusion coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def lin_sde(x, lam):\n",
    "    return lam * x, σ2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Next, we describe the probability model as a set of three stochastic variables, `lam`, `xh`, and `zh`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "button": false,
    "nbpresent": {
     "id": "4f90230d-f303-4b3b-a69e-304a632c6407"
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    \n",
    "    # uniform prior, but we know it must be negative\n",
    "    lam = pm.Flat('lam')\n",
    "    \n",
    "    # \"hidden states\" following a linear SDE distribution\n",
    "    # parametrized by time step (det. variable) and lam (random variable)\n",
    "    xh = EulerMaruyama('xh', dt, lin_sde, (lam, ), shape=N, testval=x_t)\n",
    "    \n",
    "    # predicted observation\n",
    "    zh = pm.Normal('zh', mu=xh, sigma=5e-3, observed=z_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "nbpresent": {
     "id": "287d10b5-0193-4ffe-92a7-362993c4b72e"
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Once the model is constructed, we perform inference, i.e. sample from the posterior distribution, in the following steps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [xh, lam]\n",
      "Sampling 2 chains: 100%|██████████| 6000/6000 [00:28<00:00, 210.97draws/s]\n",
      "/Users/twiecki/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(2000, tune=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Next, we plot some basic statistics on the samples from the posterior,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "button": false,
    "nbpresent": {
     "id": "925f1829-24cb-4c28-9b6b-7e9c9e86f2fd"
    },
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(10, 3))\n",
    "subplot(121)\n",
    "plot(percentile(trace[xh], [2.5, 97.5], axis=0).T, 'k', label='$\\hat{x}_{95\\%}(t)$')\n",
    "plot(x_t, 'r', label='$x(t)$')\n",
    "legend()\n",
    "\n",
    "subplot(122)\n",
    "hist(trace[lam], 30, label='$\\hat{\\lambda}$', alpha=0.5)\n",
    "axvline(λ, color='r', label='$\\lambda$', alpha=0.5)\n",
    "legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "A model can fit the data precisely and still be wrong; we need to use _posterior predictive checks_ to assess if, under our fit model, the data our likely.\n",
    "\n",
    "In other words, we \n",
    "- assume the model is correct\n",
    "- simulate new observations\n",
    "- check that the new observations fit with the original data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 4000/4000 [00:01<00:00, 3834.44it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c231eaa90>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate trace from posterior\n",
    "ppc_trace = pm.sample_posterior_predictive(trace, model=model)\n",
    "\n",
    "# plot with data\n",
    "figure(figsize=(10, 3))\n",
    "plot(percentile(ppc_trace['zh'], [2.5, 97.5], axis=0).T, 'k', label=r'$z_{95\\% PP}(t)$')\n",
    "plot(z_t, 'r', label='$z(t)$')\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Note that \n",
    "\n",
    "- inference also estimates the initial conditions\n",
    "- the observed data $z(t)$ lies fully within the 95% interval of the PPC.\n",
    "- there are many other ways of evaluating fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Toy model 2\n",
    "\n",
    "As the next model, let's use a 2D deterministic oscillator, \n",
    "\\begin{align}\n",
    "\\dot{x} &= \\tau (x - x^3/3 + y) \\\\\n",
    "\\dot{y} &= \\frac{1}{\\tau} (a - x)\n",
    "\\end{align}\n",
    "\n",
    "with noisy observation $z(t) = m x + (1 - m) y + N(0, 0.05)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c230bfb00>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N, τ, a, m, σ2 = 200, 3.0, 1.05, 0.2, 1e-1\n",
    "xs, ys = [0.0], [1.0]\n",
    "for i in range(N):\n",
    "    x, y = xs[-1], ys[-1]\n",
    "    dx = τ * (x - x**3.0/3.0 + y)\n",
    "    dy = (1.0 / τ) * (a - x)\n",
    "    xs.append(x + dt * dx + sqrt(dt) * σ2 * randn())\n",
    "    ys.append(y + dt * dy + sqrt(dt) * σ2 * randn())\n",
    "xs, ys = array(xs), array(ys)\n",
    "zs = m * xs + (1 - m) * ys + randn(xs.size) * 0.1\n",
    "\n",
    "figure(figsize=(10, 2))\n",
    "plot(xs, label='$x(t)$')\n",
    "plot(ys, label='$y(t)$')\n",
    "plot(zs, label='$z(t)$')\n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now, estimate the hidden states $x(t)$ and $y(t)$, as well as parameters $\\tau$, $a$ and $m$.\n",
    "\n",
    "As before, we rewrite our SDE as a function returned drift & diffusion coefficients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def osc_sde(xy, τ, a):\n",
    "    x, y = xy[:, 0], xy[:, 1]\n",
    "    dx = τ * (x - x**3.0/3.0 + y)\n",
    "    dy = (1.0 / τ) * (a - x)\n",
    "    dxy = tt.stack([dx, dy], axis=0).T\n",
    "    return dxy, σ2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "As before, the Euler-Maruyama discretization of the SDE is written as a prediction of the state at step $i+1$ based on the state at step $i$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can now write our statistical model as before, with uninformative priors on $\\tau$, $a$ and $m$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "xys = c_[xs, ys]\n",
    "\n",
    "with pm.Model() as model:\n",
    "    τh = pm.Uniform('τh', lower=0.1, upper=5.0)\n",
    "    ah = pm.Uniform('ah', lower=0.5, upper=1.5)\n",
    "    mh = pm.Uniform('mh', lower=0.0, upper=1.0)\n",
    "    xyh = EulerMaruyama('xyh', dt, osc_sde, (τh, ah), shape=xys.shape, testval=xys)\n",
    "    zh = pm.Normal('zh', mu=mh * xyh[:, 0] + (1 - mh) * xyh[:, 1], sigma=0.1, observed=zs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [xyh, mh, ah, τh]\n",
      "Sampling 2 chains: 100%|██████████| 6000/6000 [02:08<00:00, 46.77draws/s]\n",
      "/Users/twiecki/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(2000, tune=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Again, the result is a set of samples from the posterior, including our parameters of interest but also the hidden states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
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L84kTsGaNMhNy8iRERiqLWX5LT09pxTRxIrW1tURGRhIcHKw5Ll26pDnVwMAAJyenG1olOTs707Vr16Y9USVJavOEEFhbWzN8+HC+NjGBb74hNiiIHj168O233zJ9+vTWHuIdV11dTWxsLBERESQkJDQbqK9vGaerq4uXlxd+fn707duXvh4edNu4EdXevdCpE3TurNRCX7qk3MWrrYV27ZTNUtzclH7SERFKiAbQ0VGOxs4f+vrUvvIKZ/z8CAkL07Sua5x9btSuXTt69+7dZKGgm5ubnLSQpN+4JwKySkmWm4EiIcS/b3V+WwrIHh4eODs7s2fPnuZPmDKF8sOH6VBSwtatW5k6depdGYcQgoKCAk1oTkpKIjExkaSkJJKTkzX1zqCsAnd2dqaXvT3vhoRgnZ+PWqWixNmZGk9PTD080LW1VS7qenrKRfz115XFg59+qixSiYiADz5QgvX8+eT07UtkdDSZ0dG0P3CA2sxMdtbWciAri8rrXtvAwIC+ffsSEBBAQEAA/v7+mJmZ3ZWfiSRJd0ZaWhqOjo6sW7eO+fv3Q0YGO199lcmTJ3PhwgX69OnT2kNsFSUlJZpJiqioKM6fP8+FCxc0wblDhw707t0bW1vbJutLbCwt6VZWRucTJ1Dt3KncaezXT+nj7OKi1DXn5yslG126gLk57N4Nu3aBry+8+qpyXa6qAmdnKpydycrKIjY2lnPnznHu3DnOnz9PWVkZAPr6+nTt2pWuXbvi4OBww1d510+6H90rAXkAcAqIQmnzBvCSEGJfc+e3lYBcUlKCqakpr7/+OsuXL7/xhLo66NyZU1268HBJCbm5uS0/SJTFLJcvX24SmpOSkkhJSaE4JQWPmhpCgLKG87W0tHBzc8PX15fAwECGDBmCk4UFqqlTlZ6j3t7Kwj8jIzAzU5r2d+8Onp7KRfy6tkfC1ZWKvn0pqqujoLKSqJoa1ufnE3rxoqaFU7du3ZoEZnd3d3mxlqQ2ZPv27UyZMoXQ0FB8ZswAJyfe6tePl19+mbKyMrn73HXq6+uJj4/n/PnznD9/npiYGE253PUt4QAsLCzw6dOH3r16YdWwMLvxsLKyatpLXwil08aCBUp4bqStrUxWLFjQpDuSWq0mPj6ec+fOERMTQ3p6OmlpaaSnp2s6bDTS0dFp0mmjsZtRz5496dq1q7weS39L90RA/qPaSkA+cuQIDz74IIcOHeLBBx+88YTTp2HgQP7j5ESYkxOHDzfblKNVqdVqCgsLKSkpoaSkRLMiPSIiguDgYPIatny1s7NjeGAgL6al4ZiWhs7ChUrLpPbtYft2eOcdJSg/8gjMmAFduyqtk3bsUML0tWu/BmcHB2qee45zHh6cCQ0lKCiI4OBgCgoKAOhoYsID/v4EBATg5eWl+cAwNzeX5RmS1AreeecdXnzxRUpLSuhgawszZvBkcTHHjx8nMzOztYd3TxBCUFxcrAnLiYmJXLhwgQsXLpCQkKBpwXk9a2tr+vXrp+km5Ovri0F1NVy8qNzd09GBN95QZpZnz4a1a6GxzagQN7YTbVCRnMzVHTuojIykrKCA8qIi8isquFhby5miImILCzEC2gOFBgaYurri4uKiKdNrPCwtLeUibemeJQPyXfTmm2+yfPlyrl69SseOHW884eWXEe+8g1W7djz2r3+xevXqlh/kXyCEID4+nuPHj3P8+HF++eUXTYh1cHBg8ODBDBkyhCFDhmBnZ3frJ6yvhwMHlO4ZZ8+Cg4OyynvwYIQQpB85gsG//kVtYSGPWFgQHB9/Q0cPAwMDjI2N6dSpkyY4d+3aFQ8PDzw8POjWrRv6t7MJgCRJt23u3Lls376dgsRE5a7R6tX027oVY2PjNvmL/72mcaKisaNR4xEfH8/Zs2dJSUkBlPpiT09PzcLoBx54AMeuXVG98gq89ZZS56xWK23qGjee0tNTJjI6dVL+t8vLg9jrthjQ01NCdUXFr/XP16nU1WVNz55svHaN1NTUJkHeyMio2eDs4uKChYWFDM9SmyYD8l00fvx4kpKSiIuLa/6EPn2o0NbGKDSUTZs28dRvu0XcY9RqNbGxsZrAfOLECYoatsx2dnamX79+2NraNqm3s7W1xdLSsukmAkIoPZvnzYPkZFi0CJydlQ1U9PSUC3VAAMVbt5Jw6ZJmS9j8/HzKysooLS2loKCA7OxssrKyuHz5Mmq1UpmjpaWltNFzdsbV3R0Hb2/N1tvyNrAk/TkjR46kqKiI859/Dn36IH74gY7PPMMTTzzBxx9/3NrD+9vLy8vj3LlzBAcHc/bsWUJCQrh27RoAJiYmdO3alUd0dHiwqgqzrl2xcnXFwNhY6UhUXa0E5sJC5WjfXlkYOHw49O79a4ej6mpISlLC89WrSgmdvj6sXq1MaMydS93zz1Nw5AiVx45BQgLtcnNpX1xMmpYWz9XWcuK6gN2hQwfc3d3x8fHB19cXHx8fPK7v9CFJrUwG5LtECIGlpSWjRo1i8+bNN56QkwNWVkQ9+ii9t2whLCzsL3WvaIvUajVRUVGawBwZGcmVK1eo+c0uf0ZGRvj7+zNw4EAGDhxIv379MDQ0VILwsmVKFw2AUaNgwwalRdLjjyvt5zZubHqbsLpaacpfX6+c364d1dXVJCYkkLtnD/r792MTE4NjcTHJQC+gcYmgvb097u7umtlmd3d3evfuTYcOHVrixyVJ9yxXV1el3/G0aTBpEvkHDtBl1CjWrl3LggULWnt49526ujpiYmIIDg4mOjqazMxM0tPTiY+P17SB69WrF4GBgQwaNAg/Pz9sbGz+XDitrYXly5XNrhrp6iqdN2xtwdpa2QX28mXKxo7l4pgxXKypISE1lcjISMLCwposFvT09KR3795069ZNczg6OsryOanF/dmALP+fegvp6enk5eXRr1+/5k9ouO14qn17tLW1cXd3b8HRtQwtLS08PT3x9PTk3/9Wmo80dtNonNnNysoiOjqaU6dOsWLFCoQQ6Ojo4OPjw+DBgxnz8MP4T5xIu5wcpX5ZpYLHHlN2AHz1Vc0qbfT1le23f/4ZGhvp29jAnDnomZrS6/PP6RUVpazs7t8fvLxw+egjMufP59Tw4cTGxmq23z5x4oSmq4e2tjb9+vVj2LBhDBs2TLOBiyRJivr6etLT05k0aZLS1xdIaFhP0L1799Yc2n2rsdTC09Ozyd9XV1cTEhLCyZMnOXHiBBs3btTM8KtUKqysrLCzs8Pe3h47OzvNYW9vj7Ozc/Obj+joKGtMxoyBqChlgxQvL+VuX6Nr12DVKjqsWsWAvXsZoKOjBOixY1H//DPJV65o6q1DQ0P58ccfNeV6je/H2dlZE5jd3Nw035ubm8tSDalNkTPIt7Bt2zYeeeQRZVW3j8+NJzz/PHz6KROGDycpJYWYmJiWH2QbU1xcTFBQEKdOneLUqVOcO3eOuro6TE1NGTlyJGPHjmXUqFF07txZKcNYtEiZQa6uVjqCmJnBhAkwaZLy53XrlJkLgD59YM4cePRRZedAgOnTYedOiI5WWic1aPzAj42NJTg4mCNHjhAaGoparcbAwIDAgQN5cNgwRj30EO7u7vLiLN3XMjMzsbe359NPP2VOXBz873+sX7WK+f/6F5mZmdja2rb2EKWbqK2tJSwsjKioKDIzM5scGRkZN3TVsLe3p0+fPnh7e2sOGxub278GZmUpdwBjYpRWoAcOKEF582Z44IEmpxYVFZGQkEBiYqKmPWlji9Lr70J27NgRNzc33F1dWREUhFltLeoXXsBk7lwlvN9ltbW1pKamUlJSghACIQTV1dWUl5dTXl6OlpYWBgYGGBgYYG1tjZOTk5xkuUfIEou7ZPHixXzyySeUlpY2f9tqxAgoLMShsBB/f3++//77lh9kG1dSUsLhw4fZu3cv+/btIy8vD5VKhaenJz169NAsunNwcMDBzo5OZmaorq9lBqWGubISevW68QWys6FbNwgIUNrT/c5Fvri4mBMnThDzww88+sMP5NXUMBiw7NqVoUOHahru9+jRQ9bQSfeVkydPEhgYyMGDBxmxfj0kJvLvBx/kf//7H2VlZfIXyHuUEIKioiJNYI6Pjyc8PJywsDASExM1C6TNzc01YdnDw0Oza5+tre2td+w7dgxmzoTLl5WSuTFjYOhQZcFgo/p6SEyEsDBwdKS+Xz/NVtzXHw+GhvJiaSnJgAuQ0a4dCRYWmGtpYapWc83OjstTp2LUty9WVlZYWloqpXy3oa6ujtzcXK5cuaJZV9R4xzEpKUnTkvR2aGlp4eDggJubW5OjW7du2NraypZ5bYgMyHfJgAEDEEJw5syZ5k+wsaFm0CD0tmzhrbfeYtmyZS07wHuMWq3mwoUL7N27l3PnzhEbG0tGRkaTc4yMjDR9Oq8/Gpvdd+7c+cYP6w8/hOeeU74+8AAYGkJJibIYJTlZWYgyerRyy/DHH5WLuK4uFBURM3gwL5uYcPr0ac1OVTo6Ospshrs73t7eDBw4ED8/P9k5Q/rb2rx5MzNmzCAxMRHXqVPB2ppR9fXk5+dz4cKF1h6edBeUl5dr6ocbQ3NMTMwNrejMzMyws7PD1dUVX19f/Pz88PHxwbjxLh4oJXEvvADffacsFlSplLrlxp0Cr1xRSjQaTZumLAy0svr176KiwMeH2oce4txzz5G/cSPuu3fTsbSUfKCgtpa+gBHKdryvAmGAsbExhoaGmpnf5g61Wk1ZWZlmoTeAvpYWU62t6WVhgZW9PdZduyK8vKhqKPfQ19fHyMgIIyMjhBBUVlZSUVFBZmYmiYmJmv0GEhMTm+y2aGhoqCkvHDJkCH369MHExOQO/i8n/REyIN8FtbW1GBsbM2/ePN5/v5ldsa9ehU6duDR3Lk6ffsrPP//M2LFjW36g97iysjJSUlI0ze3T0tKaHMXFxU3ONzQ0xNXVVVOb5+npiWePHnQeM0bpxfxb2tq/tjXq0kVpf9Svn9K7+cMP4b33YNs2xMMPk5qayrlz54iMjNTMLCQnJwOgp6dH3759GThwIIMGDaJ///6yY4b0t7FixQpef/11Kisr0bOygkcfxWHfPvr378+3337b2sOTWkh1dTUZGRlkZmZy+fLlJl9jY2O5dOkSoNQ6d+vWDT8/P01o9vLywqBdO2U31iNHlFr2ujplAWDnzuDjo2xA9eOPsHKlUt/83HNKmZyjo3JdvnJFKd3o3PmGsanVagoTE6lbuxazb7+lXVkZwYGB7PDwoLymBm0hcMvOpkZXlwxLS1RaWqhUKs3RsWNHrK2t8czKwj0kBOOgIFRlZU1fREtLmUyZM0cZb12d0lLP3v7XTiC//rBAVxcBZGdnk5iYSHx8PHFxcQQFBREWFqYJ5FZWVri7u9OvXz+GDh1K//79bz0zL90RMiDfBWFhYfj4+LBlyxYeeeSRG09o2CDk53nzGLd+PRkZGbfXJ1j6Q0pKSm4IzvHx8Vy8eJErV65oznO2tGSyvT3uDg642thg37071oGBaDs5QVGRUn5x4ICyucnrrysX59paGDRIuSCHhTWpYW5UWFjI6dOnNTXVFy5coL6+Hl1dXYYNG8a4ceMYN26crNGU7mlPPvmksiFITAyYmFDzxhvo/d//8dprr/HKK6+09vCkNqKgoIDQ0FDNDoLnz58nJycHUBbh9ezZk759+9K3b1/8/Pzw8PBovnNFUpISjvfuVf5sba2E459+gn/849YDKSmBZ59V6p69vJT1KT/9pFzrQem//8gjynoVT09lRru0VFnzsnkzWFrCuHHK4eKifBZUVsKePUqXpYb3pNGvn7JRi4WF8uczZ2DiRCVE79wJzYTdkpISzpw5Q1RUFHFxccTExBAREUFdXR26urr06dMHX19fzdG9e/emrVKlO0IG5Lvg888/Z86cOaSmpuLo6HjjCZ99BnPn8tL06azft4+ioiJZp9fC8vPzuXjxYpMjNjZWU0tmYGBAz5498ff3Z9y4cQwaNAjdxh2oGmVkKBdYIZTdAefNA3NzpYfz4cPK7MHAgUqQ7tqV8mvXCA4OZv/+/ezevVvT3N/b25vx48czcuRIfHx8bnwdSWrDBg4ciEql4uS6ddC7N2lvv43jiy+ydetWpk6d2trDk9qwrKzsvIMuAAAgAElEQVSsJoH5/Pnzmjt/jeUGPj4+eHt74+Xlhbu7+69rPLKylLt5O3aAr69SdvFHNO4uWFUF48fDww8r4XnLFuX6XVenrFGZOBG2bYO0NHj5Zfi//7v54r/aWmUy5coVpWPS1avwyivKHch9+5Q7lU8/rXxOXLmi9JretUsJyXl58Omn4O8Pzey8W1ZWxunTpzl27BghISGEhYVpyjMMDQ3x9vZmwIABDBs2jAEDBshZ5jtABuS74Nlnn+XLL7+ktLS0+eDb0H0hoGdPdHR1OXHiRMsPUrpBTU0NcXFxmsDcuJ12ZWUlxsbGjBo1inHjxjFmzJhf2x1FRio7VO3YoVxQtbSUYGxsrHzfWOYxapRyTsOikMZdCPfs2cPu3bsJCgpCCIG+vj79+vXT9IT29/f/tQ9zXZ1y0ZWkNsTW1pbhw4ezafJkGD+eI//9Lw8uX05ERMQNbcYk6fcIIUhOTiYkJITz588TEhJCRESEppuGrq4uPXv2xMvLSxOae/fu3bSm+Y9oLIP47aREQYEyu7tlC/zyi3L38JtvlBahf1RoqDLbXFqq9PYPDFSee/duJSwPG6bMVK9fr/y7SqWUkbzwwq8Lx3NylIBeWKh8pvj6Uu/iQlJSEqGhoYSGhmp+ZnV1dejp6REQEKBpT+rr6yv7SP8JMiDfBcOHD6esrIxz5841f8LQoYiKCoxjYpgxYwZr165t2QFKt62iooKjR4+ye/dufv75Z3JyctDW1mbgwIE8/PDDTJo0CSsrK+UCtnGjcqtt5EjltpqWllKCsXu3MuswZIhyG66ZldP5+fmaUoxTp04RHh6OWq3mAZWKhZaWDNLRwTo7G9WgQah+/BHk5iVSG1BdXY2BgQGvvvoqr5qZwcKFrFu+nAX//S8lJSV/PrhIUoP6+nqSkpIIDw8nIiKC8PBwwsPDm/RJdnNzo2/fvvTr14++ffvi6el551qpFRUpi7Vv4/mEEJSUlFBSUkJFRQUVFRXU19ejn5eH0/LlqD080PvsM/Qar9+bNytdPFQqpZ76+eeVntJbtyolHn5+sH07BAff+GIjRiiTbaNHa2qcy8vLOXXqFEePHuXo0aNEREQAymLEwMBATWDu0aOHvGt9G2RAvgusra0ZOXIkGzdubP4ECwtKAwMx+eEHPv/8c/75z3+27AClP0WtVhMaGsru3bv58ccfiY2NRaVS4evry+DBgwkMDGTAgAHNrzr+5hulA0ZgoLKZyS3aC5WVlZH84Yf0WrGCeiE4LwRxwEyg0NWVjkFB6DWzGEWSWlJiYiLdunVj8+bNPBkZCevWMX/GDLZu26bp7CJJd5oQguzsbE1YDg0N5dy5c5qaZh0dHby8vPDy8tJsKOLk5ISdnd0d2Rm1oKCA8PBwYmNjNb2a09PTycrKuqF3dHPMzc1xcnKiW7duDDUwwK1/f/pMnaqEeiGUkPzSS8r3Xl4webKySNHMTNkK/Kef4JNPlFalzs6wYIEStH/z2ZOfn8/x48c1gbmxrM/CwoKhQ4cycuRIRo4ciaWl5V/+mfwdyYB8h129epVOnTqxatUqli5deuMJ+fnQpQtRM2bQe9Mmzp49e/Pd9qQ2LTY2lh07dnDo0CHOnTtHbW0tWlpaeHl5MXjwYIYOHcrgwYMxMjJSHtAYkh0dlZXOTz2l1KY158ABZcFJ795w6BBZFRXs3r2b5JUreSczkzAdHU68+CIzFy1SNk6RpFZw8OBBRo0axcmTJxm4Zg1ERjLG2Znc3FzZ4k1qUUIIsrKyOHfuHCEhIZw7d47o6OgbflHr2LFjk10CTUxM0NLSuumhUqkoLS0lJyeH7OxsYmNjuXz5cpPna+zHb2Njg7W1NZ06dcLQ0BADAwO0tbURQlBfX09hYaFmF9mUlBTi4+PJysoClDalQ4cOZciQIQQEBOBtYICuoWGzC8ABpd55505YswaCgpRZ7mHDlHal/fopgdrUtMlD0tPTNWH5yJEj5OXlAeDl5cWoUaMYNWoUAQEBspd/AxmQ77CgoCD69+9/89Ztv/wCQ4bw/YwZTN+0idLS0jvyG63UuioqKjh79iwnTpzgxIkTnD17lurqanR1dRk4cCBjx45l0qRJdI2JUerLTp9WFnoMG6bMKgcGKu2JcnMhNla5debhoSz4u+4iJ4Qg8pVX6Pnmm5wSggn6+jz61FMsWrQIDw+PVvwJSPej9evXM3/+fGXHvIkToVMnPDIzcXd3Z8eOHa09PEmisLCQhIQE0tLSbtgtMDMzk/LyctRqdZPjt3R1dbG0tMTCwgJXV1fNboI9e/b8y1tdl5aWcuLECQ4cOMDBgwc1s7z6+vr079+fESNGMGLECDw9PW/+OhcuKIv/T5xQNlVpZGOjTLIMHqwsNnR11fyTWq0mMjKSAwcOcODAAc6cOUNdXR0dOnRg2LBhmsDctWvXP/3e7nUyIN9hX3zxBbNnz755B4t162DBAp6bMoWtp083aTcm/X1UVVVx6tQpDh48yIEDBzRbifv4+PD444/zjL8/HbZuVWaK4+JufAIvL6UfqJlZ8y/w7bfw+OMEu7gwJCOD6poaBg4cyNy5c5k0aZLcmERqES+88AIfffQRlZWVaFlaIv7xD4y+/ZZ58+ax+o92FZCkNqJxgxC1Wk19fT16enotVrN75coVgoKCOHPmDEeOHCE6OhpQyiIefPBBRo4cyYMPPohFY9u43yoqgvPn4eJFZQOViAhoeA569FCC8oQJSnu7wkKlXGPPHupKS8m/do3Mq1c5lZ/PwZISQoB2Zmaa3f4cHR2xs7PD3t4ee3t77Ozs/tbdMmRAvsOee+45Pv/8c8rKyprfMnL+fPj+ewZ4eKClrc3JkydbfpBSi0tOTubHH39k+/bthISE0L59e2bOnMnTTz+Np5UVqqAgKC9XemVaWIC7+40rq3/rv/+F//s/ri1Zwjpzcz7//HNSUlLo2LEjU6ZM4YknnqB///5y61LprpkyZQqRkZEkhIVB+/aUL1tGh5UrWbNmDQsXLmzt4UnSPe/KlSscOnSIQ4cOcfjwYc3iRC8vL0aMGMFDDz1EQEDA7/dBTk9XgvBPP8HJk0rnDktLpeSzvh6cnJTPnYoKKC1FpKWhash4JQYGZOrokFhby/eVlfwI1F/31J07d8bFxUVT692tWze6d++Os7PznVso2UpkQL7DRo4cSWFhITd9/UGDQK3GMjmZsWPHsmHDhpYdoNTqwsLC+Oijj9iyZQs1NTV06dKFBx98kIceeohx48b9WrN8K0IobYI2bYL161HPns3Ro0f56quv2LlzJxUVFbi5ubFw4UKeeuopWcoj3XG+vr507tyZAx98AB4epLz2Gi6vvsru3bsZN25caw9Pkv5W1Go14eHhmsB85swZamtrsbCwYMKECUyaNInBgwf/fi/9ggKlm9LBg0ownjJFuWN5/Qx5SYnSni4kBJKTlRZzcXGQnU2trS3pEyYQZ2tLXFUVqdnZJCUlER8f3+SOuLa2Nj4+PgwbNozhw4cTEBBwz93Z/LMB+Xf3Lm/tw8fHR7QWW1tb8cQTTzT/j2q1EJ06ieoZMwQgVq5c2bKDk9qU3NxcsWnTJjF9+nRhbm4uAGFkZCSmTZsm9uzZI6qrq2/9JNXVQoweLQQIsWCBEDU1QgghysrKxObNm0W/fv0EIDp06CCeffZZkZSUdJfflXQ/6dSpk5g7d64Q+/YJAeLoa68JQERGRrb20CTpb6+kpERs2bJFTJ06VRgZGQlAdOzYUTzxxBNi165doqqq6s69WF2dEDt3ChEQoHzeNB42NkKsWiVEXZ0oLS0VoaGh4ptvvhHLli0TAQEBQltbWwBCX19fDBs2TKxcuVKEhISIurq6Oze2uwQIFX8ig7Z6CP69o7UCcklJye8H3+xsIUBkLF0qALF9+/aWHaDUZtXX14tffvlFzJ49W3Tq1EkAwtTUVPzzn/8UZ86cEWq1+uYPrq0VYvFi5T/LgQOF+E0IPnv2rHjssceEjo6OUKlUYuzYseLgwYO//5ySdAvFxcUCEO+8844Qa9cKAeLjl18WgCgpKWnt4UnSfaWiokLs3r1bzJgxQ5iamgpAGBsbiyeffFLs3bv39iZcbtfFi0J8+60Qb7whxMiRymfP4MFCpKffcGpJSYnYs2eP+Pe//y169eolAE2Qnzhxovj4449FfHx8m/w8kgH5DgoODhaA2LVrV/MnHD4sBIhjy5cLQFy8eLFlByjdE6qrq8WePXvE9OnTNbMC3t7eYuPGjaKysvLmD/zuOyEMDJT/PB0chJg5U4gzZzT/fOXKFfHqq6+KLl26CEB0795drFu3TpSVlbXAu5L+bsLDwwUgtm3bJsSzzwphZCTmzZ0rOnXq1NpDk6T7Wk1Njdi/f7+YMWOGMDEx0Uy4PP300+L48eOivr7+zr2YWi3Exo1CtG8vhImJEDfLPw1ycnLEd999J5555hnRtWtXTWC2sbERTz75pPjqq69EVlbWnRvfXyAD8h20YcMGAYjk5OTmT/jwQyFAfPDiiwIQ5eXlLTtA6Z5TVlYm1q9fLzw8PAQgOnfuLJYtWyYyMjKaf8ClS0KsWSPExIlCmJoKoVIJsXSpENcF66qqKvHVV1+JIZ6eYh6ImQYG4oVFi0RKSkrLvCnpb2Hnzp0CEOfPnxdi7FghPD3F6NGjRZ8+fVp7aJIkNaiqqhJ79uwRTzzxhOjQoYMAhJOTk3jjjTdu/jnyZ6SkCOHjo3zmfPihEpyFUL5GRwtx5cqvfyeEENeuCXVcnEhOSBCffvqpmDJlijAzM9MEZnd3d7FgwQLx448/iuLi4js3zj9ABuQ7aPHixUJfX//mtTX//KcQnTuLp558UlhbW7fs4KR7mlqtFkePHhUTJkwQWlpaQltbWzz66KMiOjr65g8qKxNi7lzlP9eePYX45BMhvvlGiO3bhZg5U6j19UVjHVkRiI9BLBo7Vly6dKnF3pd071q9erUARGFhoRBubkJMnizc3d3FpEmTWntokiQ149q1a+Kbb74RQ4cOFYBQqVRi5MiRYuvWrXemXvnaNWVyBoSYM0eIl14SwtFR8zkjOnUSwt9fCCcnJUiDEqovXBBCKKWGYWFh4t133xUjR44UhoaGAhCfffbZXx/bnyAD8h00evRo4eXldfMT/P2FCAwUAQEBIjAwsMXGJf29XLp0SSxZskS0b99eAGLy5MkiPDz85g/Yt08Ia+tfL1IghJGRcgGLiBDiyBFxbcIEUaOtLUpBPNaunXjxxRdb7bd26d6wYMECYWxsLNQ1NULo6Aj1Cy8IAwMD8fzzz7f20CRJuoXU1FTx6quvCnt7ewGITp06iQULFoiwsLC/9sT19UIsWaJ8zmhrKzXKX3yhrFOYPVuIwEAhHnlEiNdeU2aaLSyE0NIS4vnnhSgoaPJUVcXFIm7ZMpEXFfXXxvQnyYB8B9nb24vp06c3/49qtRDGxkLMny/Mzc3FrFmzWnZw0t9OQUGBWL58uTA2NhaAGD9+vHK7uzk1NcotroQE5bf15sJvRoao8vERAsQ6EBYmJmLFihWiqKjo7r4R6Z40duxY4enpKURqqhAgSt5/XwBizZo1rT00SZJuU319vTh8+LCYNm2a0NPTE4Dw8vISa9asEQW/Cax/yMWLQuTk3Pq8oiIlOIMQenpCPP64EHv3KqWBZmbK37fSNeXPBmS588BvlJWVkZGRcfPtfrOyoLSUSmdn8vPzcbnZ/uqSdJvMzMx44403SE9P57XXXuPUqVP4+fkxZswYgoODm56sowNWVuDmpuygZGJy4xPa2aEXHAwvvMB84LxazcEVK3BwcODtt9+mtra2Rd6XdG+4dOmSsltoUhIAWQ07ajW7g6gkSW2SlpYWw4cP57vvviM7O5t169ahra3NokWLsLa2ZtSoUbz//vvExMQos6O3q3dvZfORWzE1VbbJjoyEZ56BXbtg7Fh4/31li+wjR2DBgj/9/lqDDMi/ER8fD0CPHj2aP6Fhq8eMhs0aXK/bE12S/oqOHTvyyiuvkJaWxltvvcX58+cJCAhg+PDhnDhx4o89mY4OvPMOHDyInakpZ1QqvjUz4+1ly+jTpw9BQUF3501I9xQhxK8BOTkZgKSGf3NwcGi1cUmS9OeZmpoyf/58QkNDiYiIYMGCBaSnp7N48WJ69uyJqakpQ4cOZenSpRw/fpz6+vpbP+nt6tUL1q2DK1eUkJyeDtu3w7BhTTcxuQfIgPwbsbGxADefQY6JUb40/FEGZOlOMzY2ZtmyZaSlpfHee+8RHR3N4MGDGTRoEIcPH/5jv/2PGAHR0agWLOChtDQK27VjdXIy6/r35/k5c7h27drdeyNSm5ebm0tlZeWvM8gGBsSXlADQtWvXVh6dJEl/laenJ6tXryYuLo709HQ2bNjAtGnTKC8vZ+3atQwdOhR7e3sWL17MhQsX/tjny+9p3x7GjwcbmzvzfK2gRQOySqX6UqVS5alUquiWfN0/om/fvrz77rs4OTk1f0JMDFhaEpOTA4Czs3MLjk66nxgZGbF48WIuXbrEmjVrSE1NZcSIEfj7+7N3797bv5B16ABr1kBYGNoLFzLczIxvgcWff84bTk4EnTp1V9+H1HZdunQJQLneJSeDiwtp6emYmZnJLc0l6W/G3t6ep59+mvXr1xMSEkJRURFbt27Fz8+PtWvX4uvrS7du3VixYgUJCQmtPdxW19IzyJuAUS38mn+Iu7s7S5YsoV27ds2fEB0NPXqQnJyMra0thoaGLTtA6b5jYGDAwoULSUlJ4dNPPyUnJ4eHHnoIX1/fPxaUvbzg/ffRysiAY8fo4O7O23l5GA4axHtPPilnk+9DjQFZU2Lh6kpaWposr5Ck+4ChoSFTp07lp59+Ijc3ly+++AI7Oztef/11unfvjq+vL6tXryYrK6u1h9oqWjQgCyFOAkUt+Zp3lFoNsbHQsydJSUlygZ7UovT09JgzZw5JSUl8+eWXlJaW8tBDDzF8+HAiIiJu/4m0tGDIEIxjYqj88kscDQ2Z+PXX+Lq7s3///rv3BqQ2pzEgO9jZQWqqMoMsA7Ik3XdMTU2ZNWsWR48e5fLly7z//vtoaWmxZMkS7OzsGDJkCF988QVFRfduhPuj2lwNskqlmq1SqUJVKlVofn5+aw+nqYwMuHYNevQgKSlJ1h9LrUJHR4eZM2cSGxvL2rVruXjxIn369GHmzJl/7Dd9lQqDmTMx2b8fZ+Dl8nLGjBnDxIkTNYtVpb+3S5cuYWFhgWFhIdTUIJydZUCWpPuctbU1zz33HCEhISQmJrJixQqys7OZPXs2lpaWjB8/ni1btlBVVdXaQ72r2lxAFkJ8LoTwFUL4mpubt/ZwmmroYFFmb09BQYEMyFKr0tHRYcGCBSQnJ7NkyRK+++473NzcePXVVykvL7/9Jxo0CBYt4vGrV/m6YQahR48ezJ49+769tXa/SE1NbdLBotjcnMrKShmQJUkClEYEr7zyCnFxcYSFhfHss88SFhbGtGnTcHFxYe3atX/boNzmAnKb1tDBIllPD5AdLKS2oWPHjqxatYr4+HjGjRvH66+/jqurKxs2bLj99j1vvQXOzjx+7BgpkZEsXLiQTZs24erqyksvvURxcfHdfRNSq/htD+S0hrUXMiBLknQ9lUqFt7c37777LhkZGRw8eBAnJycWLVqEk5MT69ev/9v12JcB+Y+IiQFbW+KzswEZkKW2xdHRkS1bthAcHIyjoyOzZs3C29ubI0eO3PrBRkbw5ZeQmor5tGl8+MQTJCQkMGnSJFauXImzszMffPAB1dXVd/+NSC2irq6OzMzMXztYGBiQUFYGyIAsSdLNaWlpMWLECE6ePMkvv/yCi4sL8+fPp1evXuzatevOtYprZS3d5u17IBjoplKpLqtUqmda8vX/suho6NmTuLg4tLW1ZYs3qU164IEHOHPmDNu2baO8vJwHH3yQiRMnkpqa+vsPHDQIvvlGWazl54fjG2/wzapVhIWF4ePjw/PPP4+Hhwfbt2//21wA72eZmZnU19f/OoPs7ExSSgog21dKknR7AgMDOXHiBLt27UKlUjFhwgRGjx5968+be0BLd7GYJoSwEkLoCCFshRAbWvL1/5L6eoiLgx49iI6OxtXVFX19/dYelSQ1S6VSMWXKFGJjY3nrrbc4fPgw7u7uvPTSS79fn/zYY5CYCIsXK2HZ2RnvzZs5tHkzBw4cwNDQkClTphAYGEhUVFTLvSHpjruhxZuLC4mJidjZ2WHQsN20JEnSrahUKsaPH09UVBRr1qwhKCiIHj168Pbbb9/TZReyxOJ2paZCVZUmIPfs2bO1RyRJt6Svr8+yZctITEzkkUceYeXKlbi5ufH111+jVqubf5CJCbz7LsTHw7Rp8PHH4OTEyFOniAgO5rPPPiMmJgZvb2+ef/55yhpuy0v3Fk1AtreHlBRwdSUpKQk3N7dWHpkkSfeidu3asXDhQmJjYxkzZgzLli2jT58+BAUFtfbQ/hQZkG9XwwK9KhcXkpOTZUCW7inW1tZ89dVXBAUFYWtry5NPPsmQIUNIalic1SwnJ6UuOSEBJk+GN99E29OT2fb2JCYm8swzz/Dhhx/i5+dHTEzMzZ9HapNSU1PR1tbGTqWCmhpwcZHtKyVJ+stsbW3ZsWMHu3btori4mP79+zNv3rx7brG3DMi3KzISVCritbQQQsiALN2T/P39OXv2LF988QUXL16kd+/evPfee7/f7cLZWSm3OHYMdHRg9GjMxo3js549Ob1jB8XFxfTt25fvv/++5d6I9JddunQJOzs72qWlAVDSpQtFRUUyIEuSdEeMHz+e2NhYnnvuOT7//HO+++671h7SHyID8u0KDwc3NyIbFrHIgCzdq7S0tJg1axaxsbGMGDGCpUuX4ufnR3Bw8O8/cMgQuHgRVq+G8nJYtIiAhx8m8Zln8PHxYfr06SxcuJCampqWeSPSX3Lp0iWlg0XDpjDJWsrHgSyxkCTpTunQoQPvv/8+ERERzJkzp7WH84fIgHy7IiLA25vo6Gj09PTkKm/pnmdtbc1PP/3E1q1byc3NJSAggKeffpq8vLybP0hPD55/XrmjEh0NEyZg/NZbHJs9myVLlvDxxx8zaNAgMjMzW+6NSH+KpgdyXBx06EBsw+1POYMsSdKd1qtXL7S1tVt7GH+IDMi34+pVSEsDLy+ioqJwd3enXUNDfUm6l6lUKqZOnUp8fDxLly7l66+/plu3bqxbt+7Wm4z06AHffQcDB9Ju1izenTSJ7du3ExsbS58+fW6v/7LUKioqKsjNzVUCcmwseHiQmJSElpaW8neSJEn3ORmQb0dEhPK1YQZZlldIfzcdOnRg1apVREZG4uPjw4IFC/D19b316mM9Pdi5E2xt4R//YLKPD6GhoVhaWjJixAjefPPNm3fLkFpNWkPdsWYG2d2dpKQkHB0d0dXVbd3BSZIktQEyIN+OhoBc4ujI5cuXZUCW/rbc3d05fPgw27ZtIz8/n/79+zNz5szfL7vo3Bl+/lnphDB1Km6Ojpw9e5bp06ezfPlyxo8fz9WrV1vuTUi3lNKwlsKlc2fIydEEZFleIUmSpJAB+XaEh4O1NdENIUEGZOnvrHGTkfj4eP7zn//w7bff4ubmxtq1a6mrq2v+Qd27w//+B+fPwyuvYGRkxNdff80nn3zCoUOHGDhwIFlZWS37RqSbamzL597wZyEDsiRJUhMyIN+O8HBNeQXIgCzdH9q3b8/bb79NZGQkfn5+LFq0CF9fX86cOdP8Ax5+GP75T3jnHTh2DJVKxbx58zh48CDp6ekMGDDg9/suSy0mKioKOzs7OjQspiwwN6esrEx2sJAkSWogA/KtVFUpNXpeXkRHR9O+fXvs7e1be1SS1GK6d+/OoUOH+OGHHygsLGTAgAHMnz+fioqKG0/+4APo1g0efxwKCgAYMmQIx48fp7y8nAEDBhAZGdnC70D6Lc1airg40NMjvqoKkB0sJEmSGsmAfCvR0VBf32SBnkqlau1RSVKLUqlUPPzww8THx/P888+zfv16/Pz8bgy7RkawZQsUFsLEidAQon19fTl16hS6uroMHTqUqKioVngXEkBtbS1xcXH06tVLCcjdupGUmgrIgCxJktRIBuRbCQ8HQHh6EhUVJcsrpPuakZERq1ev5uDBgxQWFtK3b1+++OKLpid5esJXX8GZMzB1KtTWAspM9PHjx9HX12fYsGHExsa2wjuQEhMTqa2t/TUge3iQmJiIjo4OXbt2be3hSZIktQkyIN9KRAQYG5NnZERhYaEMyJIEjBgxgsjISAYPHszs2bNZuHAhtQ1BGIBHHoH162HvXpg5Expavbm4uHDs2DHatWvH0KFDSUxMbKV3cP9qXEvRy9lZ6e/esEDP2dn5nmvkL0mSdLfIgHwr4eFK/XHDbFevXr1aeUCS1DZ06dKFvXv3snjxYj7++GNGjRpFUVHRryfMmQNvvgnffgu+vvDpp1BSgpubG8eOHUOtVvOPf/yDsrKy1nsT96GoqCi0tbVx19ICIWSLN0mSpGbIgPx76uvh4kXw8iK8odRCziBL0q+0tbV577332LRpE6dPn2bw4MFNeyYvWwYbNigzyPPmgZUVfPst3bt3Z+vWrSQmJjJr1iyEEK33Ju4zUVFRuLm5odvQC1ndvTtJSUmyg4UkSdJ1ZED+PcnJyiIjb2+CgoJwcnKiS5curT0qSWpznnrqKfbt20dycjKDBw8mOztb+QeVCp5+WrkTc/489OmjtIKLjmbIkCGsXLmSbdu28dFHH7XuG7iPNOlgoa1NlqEhVVVVcgZZkiTpOjIg/57rFuidOXOG/v37t/KAJKntGjZsGPv37ycjI4PBgwc33RhEpVLKLLZvhw4dlBrla9dYunQpEyZMYOnSpTfvryzdMeXl5aSmpiqlYrGx4OxMUno6IDtYSJIkXU8G5N8THHSx0VcAACAASURBVAwGBqQaGJCXlycDsiTdQmBgIAcPHiQ7O5sxY8bcWF9saanUJMfFwaJFqFQqNm3ahJ2dHU8++STl5eWtM/D7ROMOetd3sGhsuefh4dGaQ5MkSWpTZED+PadPQ79+nAkJASAgIKCVByRJbV///v3Zvn07MTExPProozduTz18OLz0Enz5JXzzDSYmJmzatIlLly7xwgsvtM6g7xOa3UC7dYOkJHB3Jzw8HEtLSywtLVt5dJIkSW2HDMg3U16uLNAbMIAzZ85gYmJCjx49WntUknRPGDFiBOvWrWPfvn08++yzNy7CW7ECBg6EuXMhMZFBgwbx3HPPsX79eg4dOtQqY74fREVFYWhoiJNaDXV14O5OREQE3t7erT00SZKkNkUG5Js5d07pYtG/P0FBQfj7+6OlJX9cknS75syZw5IlS/h/9u49zMZy/+P4+2vGmZBBoqIoIqfGOJ/2lFNlJrUrW1Fce2qX0mGX7FJUii2dfpVS2akwSkRyCBGTQxi2Q7JNVKamZkhyHjPu3x/rMS1mjcMYa83h87quudZa93Ovtb7ruZ61fD3P977v119/nbFjxx67MTwcJk6EUqV8i4kcPMjw4cOpX78+/fv35/fffw9N0IXc+vXradCgAcW8aSsP163LN998Q5MmTUIcmYhI/qKMLydffQVm/F6/Phs3blR5hUgujBw5ks6dO/Pggw+y1VvOOEvNmjB+vO9KzUMPUapUKcaPH09KSgpDhw4NSbyFXdYMFsuWQalSbCxWjMOHDytBFhE5jhLknCQkQMOGLPvmG5xzGqAnkgvFihXj7bffJjw8nDvuuIMj3op6Wa65Bv75T3j9dZg+nebNm3P77bczZswYfvzxx9AEXUilpqaSmprqG6C3bBlERrLGG7SnBFlE5FhKkAPJzITly6FtW5YuXUpYWBhRUVGhjkqkQLrgggt46aWXWLx4Ma+++mr2Ds8+C1dcAQ88AIcO8cQTTwDw9NNPBznSwm3dunUAXHHppZCYCK1asXbtWsqWLUudOnVCHJ2ISP6iBDmQ9ethzx5o04avvvqKxo0bU65cuVBHJVJg3X777XTv3p1HH32ULVu2HLuxeHEYPRq2bYP/+z8uvPBC7rrrLv7zn/9k7yu5tmzZMsyMqPBwSE+HVq1Ys2YNjRs31vgKEZHj6FcxEG/BgsNRUaxYsULlFSJnyMwYO3YsxYsX56GHHsre4eqroXt3eOYZ2LGDf/3rX5QsWVK1yHkoISGBhg0bco5XVnGkRQvWrl2r8goRkQCUIAeSkAA1arBu927279+vBFkkD9SoUYNHH32UTz/9lCVLlmTvMGqUb3rFYcOoVq0aAwcOZNKkSVmlAZJ7GRkZLF26lLZt2/rqj2vV4vuDB9mzZ48SZBGRAIKeIJtZVzPbbGZJZvZosN//lHz1FbRpw6IvvwRQgiySRwYOHEj16tUZNGhQ9rmRL78c4uJgzBj49lsefvhhypQpwyuvvBKaYAuRdevWsXfvXtq1a+dLkL3yCkBzIIuIBBDUBNnMwoDXgG7A5UAvM8tf65tu3+77a9OGGTNm0KhRI2rWrBnqqEQKhTJlyjBs2DCWLVvGjBkzsncYOtQ3N/K//02lSpW4+eabmTx5spagPkMJCQkAdLj4Yvjpp6wBemFhYVoASUQkgGCfQY4CkpxzW51z6UA8EBPkGE7Mqz/+vUEDEhIS6NGjR4gDEilc7rjjDurVq8fgwYOzL0NdtSrceitMmgQ7d9K/f3/27t3Lhx9+GJpgC4mEhAQuvPBCzv/hB1+DlyDXq1eP0qVLhzY4EZF8KNgJcg1gu9/jZK8ti5nFmdkqM1uVlpYW1OAAqFMHBg5k5vbtHDlyhJiY/JW/ixR04eHhPPfcc2zatIkPPvgge4d77oGDB+E//6FVq1bUq1ePd955J/iBFhLOOZYsWfJneUXp0tC4sZaYFhE5gWAnyBag7ZhCROfcWOdcpHMuskqVKkEKy09kJLz0EtM/+4zzzz+fZs2aBT8GkUIuJiaGK664gldeeSV7LfIVV0D79vD669iRI/Tv35+lS5eyadOm0ARbwG3dupVffvnlzwF6kZHs2L2b5ORkDdATEclBsBPkZOACv8c1gZ+DHMNJHTp0iDlz5nDddddpflCRs8DM+Mc//sGaNWtYtWpV9g733OObF3nOHG677TbCw8MZN25c8AMtBI7WH7ePispaICQxMRGAxo0bhzI0EZF8K9jZ30qgrpnVNrMSwC1AgJE6obVw4UL27t2r+mORs6h3796ULVuWMWPGZN94/fVQvTq8+irVqlXj2muv5b333uPw4cPBD7SAW7JkCZUqVaLevn1w+DC0asWXX35JWFgYLVq0CHV4IiL5UlATZOdcBjAAmAtsAj50zm0MZgynYsaMGZQtW5a//OUvoQ5FpNA655xz6N27N/Hx8ezatevYjcWLw513wpw5kJRE//79SU1N5bPPPgtNsAVYQkICbdq0odicORAWBu3b88UXXxAVFUX58uVDHZ6ISL4U9PoB59ws59ylzrlLnHPDg/3+J+OcY8aMGXTp0oVSpUqFOhyRQu2uu+7iwIEDvPfee9k3xsVBeDi89RZdu3alSpUqTJ48OfhBFmBpaWls3rzZN0Bv+nRo354/wsNZuXIl0dHRoQ5PRCTfUoHtcRITE/npp59UXiESBE2bNqVFixa88cYb2QfrVa8O3brBBx8QbkZsbCwzZ87k4MGDoQm2AFq4cCEAV9WuDRs3QkwMixcvJjMzU1fIREROQAnycRITEylevDjXXHNNqEMRKRLuuusuvv32W770Vq48Rt++8PPPMG8ePXv2ZO/evcyfPz/4QRZQ06ZNo0qVKjQ5Ov9xjx4sWLCAUqVK0apVq9AGJyKSjylBPs7f//530tLSiIiICHUoIkXCTTfdRLly5Zg0aVL2jddeC+eeC+PH85e//IUKFSrw8ccfBz/IAujgwYPMnDmT2NhYis2c6Zs+r3ZtvvjiC9q0aaMSMhGRE1CCHECFChVCHYJIkVGmTBm6dOnCzJkzs5dZlCwJvXrBtGmU2L+fHj16MH36dM1mcQoWLFjA3r17uSk6GpYsgZgY0tLSWLduneqPRUROQgmyiITcddddx88//5w1P+8xbr8dDh2CDz/khhtuYNeuXYHLMeQY06ZN45xzzqHD3r1w5AjExGTVJKv+WETkxJQgi0jIde/enWLFijFjRoBp0a+8Ei6/HN59l86dO1O2bFmVWZxERkYG06dP59prr6X4rFlw/vnQrBlffPEF55xzDldeeWWoQxQRydfCQx3A6Tp8+DDJyckayX6cUqVKUbNmTYoXLx7qUEROW5UqVWjVqhWffvopw4YNO3ajme8s8iOPUHr7drp37860adN49dVXCQsLC0m8+d1XX33Fjh07uOGaa3zT5d12GxQrxoIFC+jQoQPh4QXup19EJKgK3K9kcnIy5cuXp1atWphZqMPJF5xz7Ny5k+TkZGrXrh3qcERypUePHgwaNIjk5GRq1qx57MbevWHQoKwyi48++oilS5f65veVbKZOnUqpUqXoFhYG+/ZBTAw//vgjSUlJDBgwINThiYjkewWuxOLgwYNUrlxZybEfM6Ny5co6qy4F2nXXXQfAp59+mn3j+edDkyYwfz7du3cnPDycWbNmBTnCgsE5x7Rp0+jcuTOl4+OhWjWIjs5ahfDqq68OcYQiIvlfgUuQASXHAWifSEFXr149LrnkksAJMsBVV8HSpZQvVozmzZtroF4Ovv76a7Zv387foqNh5kzo0weKFyc+Pp4GDRpw+eWXhzpEEZF8r0AmyCJS+JgZPbyFLPbu3Zu9w1VXweHDsGQJHTt2ZOXKlYH7FXFjxoyhbNmy9PjjD8jIgDvuIDk5mSVLlnDLLbeEOjwRkQJBCbKI5BvXXXcd6enpzJs3L/vGtm2hRAmYP5+OHTuSkZHB0qVLgx9kPpaamsqkSZO4vW9fSk+cCK1aQf36fPjhhzjnuPnmm0MdoohIgaAEWUTyjbZt21KuXLnACXKZMtCmDcyfT+vWrQkPD2fRokVBjzE/Gzt2LOnp6fyzXTvYtAn69QMgPj6eK6+8krp164Y4QhGRgkEJ8hlYv3495513Hhs2bAh1KCKFQvHixWnXrl3Oie9VV8F//0u5Awdo3ry5EmQ/hw8f5vXXX6dLly7UWrDA9x+Km28mKSmJlStXqrxCROQ0KEE+A88++yxLly7l2WefDXUoIoVGhw4d2LRpE6mpqdk3XnWV7/aLL7LqkPft2xfcAPOpjz/+mJSUFB6Ii4P4eLjpJihfnsmTJwOovEJE5DQoQT4DkyZN4uKLL2bixIl59poHDhygQ4cOZGZmAr55nydPnkx6ejrt27cnIyMjz95LJD/q2LEjQOBZKq68EipUgPnz6dChg+qQ/bzyyivUrVuXq3ftgr17jymvaNu2LRdccEGIIxQRKTiUIOcz48aNo2fPnlkrhC1YsIDExERKlChBdHR01tkgkcKqWbNmlCtXLnD5RFgYdOoE8+bRpnVrwsLCVGYBLFu2jGXLlnHvvfdS7K23oH59aNuW9evXs2HDBpVXiIicJiXIudSpU6esgUSPP/449913X5687oQJE4iJiQEgISGBBx98kClTptCkSRNiY2OZMGFCnryPSH5VvHhx2rZte+I65B9+oFxqquqQ8S0M8vDDD1OtWjX6R0bCihW+5aXNeP311ylZsiQ33XRTqMMUESlQCtxS0/7uv/9+1q5dm6ev2aRJE1566aWT9hs2bBhPPPEEqamprFmzhhkzZpzxe6enp7N161Zq1aoF+Eb0N2/enOeff56GDRuSmZnJypUrz/h9RPK7jh078uijj5KamkrVqlWP3Xi0Dtmb7u35559n3759lC1bNviB5gPTpk3jq6++YuzYsZR5/30oWRL69OG3335j/Pjx3HrrrVSpUiXUYYqIFCg6g5xL7du3xznHCy+8QHx8fFZJxJnYsWMHFStWPKZt8+bNXHbZZQCEhYVRokQJ9uzZc8bvJZKfHa1DXrx4cfaNl17qW3p60aIiPx9yeno6gwYNokGDBtzx17/CBx/4Buedey5vvfUWBw4cYODAgaEOU0SkwCnQZ5BP5Uzv2bJ+/XpSUlKIiIigfPnyAHzzzTcMHTqUypUrEx0dTUREBEOGDKFBgwbccsstdOzYkSlTprBmzRouuugi4uLiGDhwIP/+978pWbIkpUuX5uDBg1nvsXPnTipUqEDx4sWz2g4dOkSpUqWC/nlFgqlZs2aULVuWRYsWceONNx670Qw6doQvvqDN2LEUK1aMxYsXc/XVV4ck1lB64403SEpKYtasWYR//DHs2QN33snhw4d59dVXiY6O5oorrgh1mCIiBY7OIOdCSkoKvXv3Zvr06ZQtW5a5c+cCMHv2bO69917GjBnDe++9h5lRrlw5Dh48SM2aNQFYvXo1w4cPZ+vWrcTHx9OzZ09KliwJQKVKlcjMzMxKkrdt28b555+f9b47d+6kSpUqxyTMIoXRSeuQO3aEX36h3M8/07hx4yJ5BnnXrl0MGzaMq6++mq5du8Kbb0KDBtC6NVOnTiU5OZn7778/1GGKiBRISpBP0/79++nZsyejR4+mfv36DBkyhKFDhwJw2223ER8fz8MPP8zOnTtp164ds2fPZuTIkTz55JMA9OrViyeeeIKWLVuybt06EhMTefbZZ7OmdevcuTMJCQkA1KtXjx07dtCwYUOWLl3KwoUL6d69e0g+t0iwdezYkY0bN5KWlhZoo+920SJat27NihUritwUiAMHDmT37t2MGjUKW7kSVq7MGpz30ksvUadOHf1eiIjkkhLk01SmTBmWLVuWdTm3ffv2LFu2DICqVavy2muvMWLECCIiIihWzLd7K1WqxKFDhwBo1KgRTz31FCtXrqRPnz4457jssstITEwEYMCAAYwfPx6AcuXK8fXXX7NhwwZat27NxIkTiYuLC/ZHFgmJE86HXKdOVh1ymzZt2LdvH+vXrw9ugCE0bdo03n//fR577DEaN2oEDz0EVarA7beTkJDA8uXLGThwYNZvkIiInB79euah77//nri4OPr06cPDDz/M1KlTufPOO7ntttsYMGBAVr+EhAQaNGhA3bp12bJlC/Pnz6du3boANG3alE6dOmWdUT4qPT2d2NjYrAF7IoXdlVdeSenSpQOXTxytQ160iNatWgEUmTKLtLQ07rzzTpo2bcrjjz8OH30ECQnwzDO48uUZNGgQ5513HrfffnuoQxURKbDMORfqGHIUGRnpVq1adUzbpk2bqF+/fogiyt+0b6Swadu2LUBW2dEx3noL4uJwmzZRMzqajh07Fvp5wp1z3HjjjcycOZPVq1fT8JJLfIuCVKgAiYlMmzGDnj178uabb+pqk4gIYGarnXORp/s8nUEWkXwrKiqKxMREDh8+nH2jV4JhX35J69at+eqrr4IbXAi8/fbbTJ06laeffpqGDRvCCy/ADz/ASy9x+MgRBg0aRP369ennLTMtIiK5owRZRPKtqKgoDhw4wMaNG7NvPK4O+YcffuCnn34KfpBBsmLFCgYMGECXLl146KGH4Kef4Lnn4PrroVMn3nrrLbZs2cLIkSMJDy/QM3iKiIRc0BJkM/urmW00syNmdtqnukWk6ImKigLg66+/zr4xQB3y0QGzhc2vv/7KDTfcQI0aNZg4cSJhxYrBnXfCkSPw/PP88ccfDB06lPbt23PttdeGOlwRkQIvmGeQNwA9gQBLY4mIZFe7dm0iIiJYsWJF4A7efMhNypShVKlShXKg3uHDh7npppv47bffmDZtGueeey6MHw+ffeY7g3zxxTzyyCPs2LGD559/HjMLdcgiIgVe0K7DOec2AfrxFpFTZmZERUUFPoMM0KEDACWWLqV58+aFLkHOzMykb9++LF68mPfff5/GjRv7Sivuvx/atYN772Xu3Lm8+eab/POf/6R58+ahDllEpFDIdzXIZhZnZqvMbFXABQJEpEiJiopi48aN7NmzJ/vGunUhIgKWLaNNmzYkJiZy4MCB4Ad5FjjnuPvuu5k0aRIjRozg1ltvBefg73+Hw4dh3Dh+/+MP+vfvT/369Xn66adDHbKISKGRpwmymc03sw0B/mJO9TWcc2Odc5HOucgqVarkZXgiUgBFRUXhnMtaTOcYZtCqFSxfTuvWrTl8+DDHTw1ZEDnnGDRoEGPHjmXw4MEMGjTIt+HTT2H2bF9pRZ063H///fzyyy+MHz+eUqVKhTZoEZFCJE8TZOfcVc65hgH+pufl+4hI0XG0bCDHMotWrWDzZlrXqwcU/AVDnHMMGTKEUaNGcc899zB8+PA/N44aBRddBHffTXx8POPHj2fw4MEqrRARyWP5rsSiIFm/fj3nnXceGzZsCHUoIoVWREQEF198cc4D9Vq2BKByUhKXXnppgU6Qj545Hj58OHFxcbzyyit/jttYvty3Yt4DD7Bm/Xr69etH27ZtGTJkSGiDFhEphII5zdv1ZpYMtAI+M7O5wXrvs+XZZ59l6dKlPPvss6EORaRQa9GiRc5nkJs3h2LFsuqQly5dSn5eITQnzjkeeughRo0axd13382YMWMoVszvJ3r0aKhYkbQePYiNjaVy5cpMmTKFEiVKhC5oEZFCKmgJsnNumnOupnOupHOumnOuS7De+2yZNGkSF198MRMnTsyz1zxw4AAdOnQgMzMTgOTkZCZPnkx6ejrt27cnIyMjz95LpKCIiopi+/btpKSkZN9Yrhw0agTLltG6dWt27NjBli1bgh/kGcjMzOTOO+/kxRdfZODAgbz66qvHJsfffQdTp5IZF8eNt99Oamoqn3zyCdWqVQtd0CIihZhKLPKZcePG0bNnT8LCwgBYsGABiYmJlChRgujoaCZPnhziCEWC7+iCIStXrgzcoWVLWLGC1i1aAAWrDvnQoUP06tWLt956i3/961+8+OKL2afDfOklXFgYt69ezeLFi3n77be58sorQxOwiEgRoAQ5lzp16sS8efMAePzxx7nvvvvy5HUnTJhATIxv0o+EhAQefPBBpkyZQpMmTYiNjWXChAl58j4iBUnTpk0JCws78UC9PXuo5xwVK1YsMAny7t276dGjBx999BGjR49m+PDh2ZPj5GTcuHHMjYjggwULeOONN+jdu3doAhYRKSKCtlDI2XD//fezdu3aPH3NJk2a8NJLL52037Bhw3jiiSdITU1lzZo1zJgx44zfOz09na1bt1KrVi0A2rZtS/PmzXn++edp2LAhmZmZOZ9BEynESpcuTaNGjXIeqOctNV3s669p1apVgUiQ//vf/3LjjTeybds2xo0bxx133JG90/r1HOnWjYOHDvHgL7/w7rvv0rdv3+AHKyJSxOgMci61b98e5xwvvPAC8fHxWSURZ2LHjh1UrFjxmLbNmzdz2WWXARAWFkaJEiUCL5ggUsi1aNGClStXcuTIkewb69SBypWzBupt3LiR33//PfhBnqL//Oc/tGzZkv3797No0aLAyfG8eRxp3Zq01FTaAU9OmqTkWEQkSAr0GeRTOdN7tqxfv56UlBQiIiIoX748AN988w1Dhw6lcuXKREdHExERwZAhQ2jQoAG33HILHTt2ZMqUKaxZs4aLLrqIuLg4Bg4cyL///W9KlixJ6dKlOXjwYNZ77Ny5kwoVKlC8ePGstkOHDmlBACmSoqKieOONN9iyZUvWfxqzmPnqkJcto/WttwKwbNkyunXrFoJIc3bgwAEGDBjAuHHjiI6OZuLEiVStWvXPDvv2wfTpMGECbs4cNoeFERMezv9Nm0aXLgV+XLOISIGhM8i5kJKSQu/evZk+fTply5Zl7lzfjHWzZ8/m3nvvZcyYMbz33nuYGeXKlePgwYPUrFkTgNWrVzN8+HC2bt1KfHw8PXv2pGTJkgBUqlSJzMzMrCR527ZtnH/++Vnvu3PnTqpUqXJMwixSVBwdqHfCOuRNm2hety5hYWH5rswiKSmJVq1aMW7cOB5//HHmzp37Z3K8Zw88+SScdx707s3BVat4uUQJrjnnHCYuXqzkWEQkyJQgn6b9+/fTs2dPRo8eTf369RkyZAhDhw4F4LbbbiM+Pp6HH36YnTt30q5dO2bPns3IkSN58sknAejVqxdPPPEELVu2ZN26dSQmJvLss89mTevWuXNnEhISAKhXrx47duygYcOGLF26lIULF9K9e/eQfG6RUKtXrx7lypXLOUH2Fgwpt3EjjRs3zjcJcmZmJmPGjOHKK69k+/btzJo1i6efftpXlnXkCLzxhq9E5KmnoGtXZjz0EOfs3MmYCy/k8+XLiYyMDPVHEBEpcpQgn6YyZcqwbNkyrr76asBXi7xs2TIAqlatymuvvcaIESOIiIjImse0UqVKHDp0CIBGjRrx1FNPsXLlSvr06YNzjssuu4zExEQABgwYwPjx4wGykoENGzbQunVrJk6cSFxcXLA/ski+EBYWRvPmzXNOkKOiIDwcFi2iTZs2rFixIuTzhicmJtKqVSvuvvtuIiMjSUxMPLbs47nn4B//gPr1SV+yhH9ERBAzejRXde7MihUrqFOnTuiCFxEpwpQg56Hvv/+euLg4+vTpw8MPP8zUqVO58847ue222xgwYEBWv4SEBBo0aEDdunXZsmUL8+fPp27duoBvOqtOnTplnVE+Kj09ndjY2Oy1lyJFSFRUFGvXrs36D+cxypeHNm1gzhxat27Nvn37WL9+ffCDxDd923333Ufz5s358ccfmTBhAvPnz+eiiy76s9Pnn8OQIfC3v5E4ejTN7rqLN954g0GDBvHpp59mG7ArIiLBU6AH6eU3tWrVYuzYsce09ezZM1u/tm3bZt0fM2ZMtu39+vXL1laiRAn69OmTB1GKFFxRUVGkp6fz3//+N6sm+Rhdu8LgwbTzzrx++eWXNG3aNGjxOeeYPHkyDzzwAL/++it33303zzzzTPZk9/vvoVcvXIMGjKhdmydatqRKlSrMmjUr3w0sFBEpinQGWUQKjJMO1POSyxobNnD55Zczc+bMoMTlnGPevHlERUXRq1cvatSowddff82rr76aPTlOSoIbbiDz8GF6Av8aPpybb76ZDRs2KDkWEcknlCCLSIFRo0YNqlevnnOC3KgRVK8Os2dz3XXX8eWXX7J79+6zGtPy5cuJjo6mc+fOpKam8s4777BixYpjB9c5B3PmwDXX4C69lMz//pe/HjjAkpQUPvroIz744APOPffcsxqniIicOiXIIlJgmBktWrTIOUE285VZzJtHj+7dycjIYM6cOWcllg0bNhAbG0urVq3YsGEDL7/8Mv/73//o16/fnwsHZWTAhAm+xL1bN9JXrGBstWpckJlJZvfubNy4kRtvvPGsxCciIrmnBFlECpSoqCg2b97Mrl27Anfo2hV27aKFGREREXz66ad5+v5bt27ltttuo1GjRixcuJBnnnmGrVu3ct9992XNac6BA/Daa1C3Ltx6KxkZGbzdvj3ldu7k6bAwXpo8mU8++YRq1arlaWwiIpI3lCCLSIFytA551apVgTtcfTUUK0bYvHlcc801zJo1K0+me/v555+5++67ueyyy/j444955JFH2LZtG4899hjlypWDXbtg0SLffMYXXQQDBuDOO4/P7rqLqikp/GPpUh545BG+/fZbbrrpJszsjGMSEZGzQwmyiBQokZGRhIWF8eWXXwbuUKmSb9GQ2bPp0aMHu3bt4quvvsr1+/32228MGjSIOnXq8NZbb/H3v/+dpKQkRowY4asbnj7dd6b43HOhUyffiniRkSS++CKRhw5x7Rtv0KRZM9atW8fIkSN9ybSIiORrSpBFpECpUKEC7dq1Y/r06Tl36toVVq2iS9OmlChRIldlFnv37uWZZ56hdu3ajBo1ihtuuIHNmzfz+uuv+5aA37kTeveG2FgoWxZGjIDZs1k7hgtwSQAAIABJREFUezadMzK48oEHSE1LIz4+ngULFlC/fv0z+NQiIhJMSpBFpMCJjY1lw4YNJCUlBe7gTZdWdsECOnXqdFoJ8qFDh3j55Ze5+OKLGTJkCJ06dWLdunW8//77XHzxxb5OCxdCw4bw4YcwdCgZy5Yx7dJL6TRyJE27dWPNmjW88MILbNmyhZtvvlnlFCIiBYwS5Dx24MABOnTokLUSXnJyMpMnTwZ8q+G1b98+5MvfihR0MTExADmfRW7WDJo0geHDienWjf/9739s3rz5hK+ZkZHBuHHjuPTSS7n//vu54oorWL58OZ988gkNGzb0dTpyxHem+KqroEIFds+bx79Ll+aSevXo2bMnW7duZeTIkXz33Xc88MADlCpVKi8/toiIBIkS5Dw2btw4evbsmTXN04IFC0hMTAR8q+FFR0dnJcwikju1atWicePGfPLJJ4E7FCsGzz0H33/PLbt3ExYWxj/+8Q/279+freuRI0eYMmUKV1xxBf3796datWrMmzePBQsW0KJFiz87/vSTr5xi8GD+6NKFe1u2pHr37gwaNIhLLrmEqVOn8t133/HII49wzjnnnKVPLiIiwVCwl5q+/35YuzZvX7NJE3jppZN269SpE//617+4+uqrefzxx/njjz945ZVXmDBhAhMnTgQgISGBBx98kIoVKzJ37lymTZtGbGwsgwcPpnfv3nkbt0gRExsby1NPPUVqaipVq1bN3qFLF+jYkUqvvsoHY8bwtzvv5LrrruPTTz+lTJkyZGRk8PnnnzNkyBASExO5/PLLmTp1KrGxsceWRBw8CKNHw7PPciQjg3GNGxM3ezYlS5WiT58+DBgwgCuuuCJ4H1xERM66gp0gh9CwYcN44oknSE1NZc2aNcyYMYP09HS2bt1KrVq1AGjbti3Nmzfn+eefz7pEm5mZycqVK0MYuUjhEBsby7Bhw5g5cyb9+vXL3sHMVw7RsiW3pKSQ8d579OnTh27dulG7dm1mzpzJzp07qVWrFuPHj6d3795/LvABkJYG776Le+017IcfWFylCrenpbHrhx947PHHuffeewMn5iIiUuAV7AT5FM70ni3t27fHOccLL7zAokWLCAsL49dff6VixYrH9Nu8eTOXXXZZ1uOwsDBKlCjBnj17KF++fLDDFik0GjduzEUXXcQnn3wSOEEGaNECrr8eRo3i1u++g/feo2/fvqxbt45rrrmGmJgYYmJiKHHwIMTHw/btvsR42zbcZ59h6emsLVuWfwLfFi/OQ6NH8/e//13fXRGRQq5gJ8ghtH79elJSUoiIiMj6x7J06dIcPHgwq8/OnTupUKECxYsXP+a5hw4d0uAdkTNkZsTExPDmm2+yd+/enOcXHj4cZs6Edu24ddo0/rJ9O1WqVKF4eDisXAl33w2TJoFXn+zKlGFP6dJMLV2aUenpZNasySOPPELv3r3/XClPREQKNQ3Sy4WUlBR69+7N9OnTKVu2LHPnzgWgUqVKZGZmZiXJ27Zt882X6mfnzp2+f5yPS5pF5PTFxsZy6NAhpkyZknOn+vVh/nzYvRuiojh/wQKKv/UWNG3qO8McHw9/+xt7589n9NNPU718eSrs3Mnrl17KM1On8s0339CvXz8lxyIiRYgS5NO0f/9+evbsyejRo6lfvz5Dhgxh6NChWds7d+5MQkICAPXq1WPHjh00bNiQpUuXArBw4UK6d+8eitBFCp127doRGRnJ3XfffeLV8tq3h9WroVEj6NMH7rnHN9PFG2/w65o1PFq5MjV69uSfQ4bQuHFjvvjiC1asWMH1119PsWL6mRQRKWrMORfqGHIUGRnpVq1adUzbpk2b8vWKVEcXCHj//fcDbu/ZsyfPPffcMXXJeSW/7xuRsyE1NZW2bduSlpbGkiVL/pyzOJD0dJg8GVe/PolmjB07lvHjx3P48GFuvPFGBg0aRLNmzYIXvIiInFVmtto5F3m6z9OpkTzWtGlTOnXqlLVQiL/09HRiY2PPSnIsUlRVrVqVzz//nNKlS9OlSxemTZvGnj17junjnOOnn35iwZIljPrlF5r0709kZCTjx4+nb9++fPvtt0yePFnJsYiIAEE8g2xmo4DrgHTgO+AO59zvJ3pOQTyDHEraN1KUbdiwgauuuopff/2V8PBwWrVqhZmRkpLCzz//zL59+7L6RkZG0q9fP2655RYqVaoUwqhFRORsyu0Z5GDOYjEPGOycyzCzkcBgYFAQ319ECrGGDRvy448/snTpUubMmcPChQspWbIkTZs2pXv37tStW5f69etTv359qlevHupwRUQkHwtaguyc+9zv4XLgxjN4rWNXuhLycy25SLCUKFGCjh070rFjx1CHIiIiBVioapD7AbMDbTCzODNbZWar0tLSsm0vVaoUO3fuVELoxznHzp07NbeyiIiISB7I0zPIZjYfOC/Apsecc9O9Po8BGcCEQK/hnBsLjAVfDfLx22vWrElycjKBkueirFSpUtSsWTPUYYiIiIgUeHmaIDvnrjrRdjPrC1wLRLtcngIuXrw4tWvXzs1TRUREREROKmg1yGbWFd+gvA7Ouf3Bel8RERERkdMRzBrkV4HywDwzW2tmbwTxvUVERERETkkwZ7GoE6z3EhERERHJrXy91LSZpQE/hOCtI4AdIXjfgkj76tRpX5067atTo/106rSvTp321anTvjp1odpXFznnqpzuk/J1ghwqZrYqN6uuFEXaV6dO++rUaV+dGu2nU6d9deq0r06d9tWpK2j7KlTzIIuIiIiI5EtKkEVERERE/ChBDmxsqAMoQLSvTp321anTvjo12k+nTvvq1GlfnTrtq1NXoPaVapBFRERERPzoDLKIiIiIiB8lyCIiIiIifpQgH8fMuprZZjNLMrNHQx1PfmJmF5jZQjPbZGYbzWyg1z7UzH7yVkhca2bdQx1rqJnZ92a23tsfq7y2c81snplt8W4rhTrOUDOzy/yOm7Vm9oeZ3a9jysfMxplZqplt8GsLeByZzyveb9c6M2sWusiDL4d9NcrMvvX2xzQzq+i11zKzA37HV5Fa2TWHfZXjd87MBnvH1WYz6xKaqIMvh/002W8ffW9ma732on5M5ZQfFNjfK9Ug+zGzMOB/wNVAMrAS6OWc+yakgeUTZlYdqO6cSzSz8sBqIBa4CdjrnHs+pAHmI2b2PRDpnNvh1/Zv4Dfn3AjvP1+VnHODQhVjfuN9/34CWgB3oGMKM2sP7AXec8419NoCHkdeQnMv0B3fPnzZOdciVLEHWw77qjPwhXMuw8xGAnj7qhYw82i/oiaHfTWUAN85M7scmAREAecD84FLnXOZQQ06BALtp+O2jwZ2O+ee0jGVY35wOwX090pnkI8VBSQ557Y659KBeCAmxDHlG865FOdcond/D7AJqBHaqAqUGGC8d388vh8P+VM08J1zLhSrZ+ZLzrnFwG/HNed0HMXg+4fcOeeWAxW9f7SKhED7yjn3uXMuw3u4HKgZ9MDyoRyOq5zEAPHOuUPOuW1AEr5/Kwu9E+0nMzN8J4cmBTWofOoE+UGB/b1SgnysGsB2v8fJKAEMyPvfclNghdc0wLtMMk6lAwA44HMzW21mcV5bNedcCvh+TICqIYsuf7qFY/+x0TEVWE7HkX6/TqwfMNvvcW0zW2NmX5pZu1AFlc8E+s7puAqsHfCrc26LX5uOKbLlBwX290oJ8rEsQJtqUI5jZuWAj4H7nXN/AGOAS4AmQAowOoTh5RdtnHPNgG7APd6lOsmBmZUAegAfeU06pk6ffr9yYGaPARnABK8pBbjQOdcUeBCYaGbnhCq+fCKn75yOq8B6cex/6HVMETA/yLFrgLZ8dVwpQT5WMnCB3+OawM8hiiVfMrPi+A7+Cc65qQDOuV+dc5nOuSPAWxSRy28n4pz72btNBabh2ye/Hr2E5N2mhi7CfKcbkOic+xV0TJ1ETseRfr8CMLO+wLVAb+cNuvHKBXZ691cD3wGXhi7K0DvBd07H1XHMLBzoCUw+2qZjKnB+QAH+vVKCfKyVQF0zq+2d0boFmBHimPINr+bqHWCTc+4Fv3b/uqHrgQ3HP7coMbOy3iAFzKws0BnfPpkB9PW69QWmhybCfOmYszE6pk4op+NoBtDHGx3eEt/goZRQBJhfmFlXYBDQwzm336+9ijcoFDO7GKgLbA1NlPnDCb5zM4BbzKykmdXGt6++DnZ8+cxVwLfOueSjDUX9mMopP6AA/16FhzqA/MQb6TwAmAuEAeOccxtDHFZ+0ga4DVh/dGob4F9ALzNrgu/yyPfAnaEJL9+oBkzz/V4QDkx0zs0xs5XAh2bWH/gR+GsIY8w3zKwMvplj/I+bf+uYAjObBHQEIswsGXgSGEHg42gWvhHhScB+fDOBFBk57KvBQElgnvd9XO6cuwtoDzxlZhlAJnCXc+5UB60VeDnsq46BvnPOuY1m9iHwDb4ylXuKwgwWEHg/OefeIft4CSjixxQ55wcF9vdK07yJiIiIiPhRiYWIiIiIiB8lyCIiIiIifpQgi4iIiIj4UYIsIiIiIuJHCbKIiIiIiB8lyCIiIiIifpQgi4iIiIj4UYIsIiIiIuJHCbKIiIiIiB8lyCIiIiIifpQgi4iIiIj4UYIsIiIiIuJHCbKIiIiIiB8lyCIiIiIifpQgi4iIiIj4UYIsmFlvM9vr/R0xswPe/TdCHZuIZGdmj5rZd2a2x8y+MbPrQx2TiBzLzL43s4fNbJ2Z7TOzd8ysmpnN9r67882sUqjjlMDMORfqGCQfMbNk4Fbn3KJQxyIigZnZX4GvgF+AvwLjgDrOuZSQBiYiWczse3zf0RggHFgDJAP9gW+A2cCXzrlhoYpRcqYzyCIiBYxz7iPn3M/OuSPOucnAFiAq1HGJSDb/55z71Tn3E7AEWOGcW+OcOwRMA5qGNjzJiRJkEZECxsz6mNlaM/vdzH4HGgIRoY5LRLL51e/+gQCPywU3HDlV4aEOQPKdw4CFOggRCczMLgLeAqKBZc65TDNbi763IiJ5RmeQ5XjbgHqhDkJEclQWcEAagJndge8MsoiI5BElyHK8YcBgM5sd6kBEJDvn3DfAaGAZvsu1V+AbsCciInlEs1iIiIiIiPjRGWQRERERET9KkEVERERE/ChBFhERERHxowRZRERERMTPSedBNrNxwLVAqnOu4XHb/gmMAqo453aYmQEvA92B/cDtzrlEr29f4HHvqc8458af7L0jIiJcrVq1TuPjSEG1NW0fABdXKRviSIJv9erVO5xzVUIdR17Qdza0ivL3KFj0fT17dPzK2ZDb7+ypLBTyLvAq8J5/o5ldAFwN/OjX3A2o6/21AMYALczsXOBJIBLf/J2rzWyGc27Xid64Vq1arFq16tQ+iRRoN7+5DIDJd7YKcSTBZ2Y/hDqGvKLvbGgV5e9RsOj7evbo+JWzIbff2ZOWWDjnFgO/Bdj0IvAIvoT3qBjgPeezHKhoZtWBLsA859xvXlI8D+iam4BFREQKCzMbZ2apZrbBr+1cM5tnZlu820peu5nZK2aWZGbrzKyZ33P6ev23eFdsReQM5KoG2cx6AD855/573KYawHa/x8leW07tgV47zsxWmdmqtLS03IQnIiJSULxL9hNGjwILnHN1gQXeYzj2Km0cvqu0+F2lbQFEAU8eTapFJHdOO0E2szLAY8ATgTYHaHMnaM/e6NxY51ykcy6ySpVCUeYlIiISUA5XaWOAo+N0xgOxfu26SisSBLk5g3wJUBv4r5l9D9QEEs3sPHxnhi/w61sT+PkE7SKSx3K4ZDvKzL71LstOM7OKftsGe5dsN5tZF7/2rl5bkpk9evz7iMhZU805lwLg3Vb12nWVViRITjtBds6td85Vdc7Vcs7VwvdFbOac+wWYAfTx6qRaAru9L/dcoLOZVfIu+3T22kQk771L9rNH84CGzrlGwP+AwQBmdjlwC9DAe87rZhZmZmHAa/gu6V4O9PL6ikjo6CqtSJCcNEE2s0nAMuAyM0s2s/4n6D4L2AokAW8BdwM4534DngZWen9PeW0ikscCXbJ1zn3unMvwHi7HdxUHfJds451zh5xz2/B9d6O8vyTn3FbnXDoQ7/UVkbPvV690Au821WvXVVqRIDnpNG/OuV4n2V7L774D7smh3zhg3GnGJ0VcrUc/O63+34+45ixFUqj0AyZ792vgS5iP8r80e/wl2xaBXszM4vANGOLCCy/M00CLmpyOdx3XRc4MoC8wwrud7tc+wMzi8X0fdzvnUsxsLvCs38C8znhXiQoC/+O+Re1zQxiJyJ9OZR5kESkkzOwxIAOYcLQpQDdH4KtLOV6yBcYCREZGBuwjIoF5V2k7AhFmloxvNooRwIfeFdsfgb963WfhW4grCd9iXHeA7yqtmR29Sgu6SityxpQgixQR3tyo1wLR3tUeOPGlWV2yFTnLTnCVNjpAX12lFQmSXM2DLCIFi5l1BQYBPZxz+/02zQBuMbOSZlYb3/yqX+M7E1XXzGqbWQl8A/lmBDtuERGRUNAZZJFCJodLtoOBksA8MwNY7py7yzm30cw+BL7BV3pxj3Mu03udAfhmmwkDxjnnNgb9w4iIiISAEmSRQiaHS7bvnKD/cGB4gPZZ+GoeRUREihSVWIiIiIiI+FGCLCIiIiLiRwmyiIiIiIgfJcgiIiIiIn6UIIuIiIiI+FGCLCIiIiLiRwmyiIiIiIgfJcgiIiIiIn6UIIuIiEi+sGLbb9R69LNQhyGiBFlERERExN9JE2QzG2dmqWa2wa9tlJl9a2brzGyamVX02zbYzJLMbLOZdfFr7+q1JZnZo3n/UUREREREztypnEF+F+h6XNs8oKFzrhHwP2AwgJldDtwCNPCe87qZhZlZGPAa0A24HOjl9RURERERyVdOmiA75xYDvx3X9rlzLsN7uByo6d2PAeKdc4ecc9uAJCDK+0tyzm11zqUD8V5fEREREZF8JS9qkPsBs737NYDtftuSvbac2rMxszgzW2Vmq9LS0vIgPBERERGRU3dGCbKZPQZkABOONgXo5k7Qnr3RubHOuUjnXGSVKlXOJDwRERERkdMWntsnmllf4Fog2jl3NNlNBi7w61YT+Nm7n1O7iIiIiEi+kasE2cy6AoOADs65/X6bZgATzewF4HygLvA1vjPIdc2sNvATvoF8fzuTwEVERKRw8p8L+fsR14QwEimqTpogm9kkoCMQYWbJwJP4Zq0oCcwzM4Dlzrm7nHMbzexD4Bt8pRf3OOcyvdcZAMwFwoBxzrmNZ+HziIiIiIickZMmyM65XgGa3zlB/+HA8ADts4BZpxWdiJw2MxuHr/wp1TnX0Gs7F5gM1AK+B25yzu0y3/9wXwa6A/uB251zid5z+gKPey/7jHNufDA/h4iISKhoJT2Rwuddss9d/iiwwDlXF1jgPQbf3OR1vb84YAxkJdRPAi3wTdP4pJlVOuuRi4iI5ANKkEUKmUBzl+Obd/zoGeDxQKxf+3vOZzlQ0cyqA12Aec6535xzu/AtDnR80i0iIlIoKUEWKRqqOedSALzbql675i4XERE5jhJkkaJNc5eL5FNm9oCZbTSzDWY2ycxKmVltM1thZlvMbLKZlfD6lvQeJ3nba4U2epGCTQmySNHwq1c6gXeb6rXnNHf5ieY0F5GzzMxqAPcBkd5g2zB8U6SOBF70xhPsAvp7T+kP7HLO1QFe9PqJSC4pQRYpGmYAfb37fYHpfu19zKclsNsrwZgLdDazSt7gvM5em4gETzhQ2szCgTJACvAXYIq3/fjxBEfHGUwBor1ZakQkF3K9kp6I5E85zF0+AvjQzPoDPwJ/9brPwjfFWxK+ad7uAHDO/WZmTwMrvX5POeeOH/gnImeJc+4nM3se3/f1APA5sBr43TmX4XXzHxuQNW7AOZdhZruBysAO/9c1szh8M9Zw4YUXnu2PIVJgKUEWKWRymLscIDpAXwfck8PrjAPG5WFoInKKvCs3MUBt4HfgI3zTMh7v6NiAUxo34JwbC4wFiIyMDDiuQESUIIuIBJ3/MroiObgK2OacSwMws6lAa3xTMYZ7Z5H9xwYcHTeQ7JVkVCD7dI8icopUgywiIpL//Ai0NLMyXi1xNPANsBC40etz/HiCo+MMbgS+8K4QiUguKEEWERHJZ5xzK/ANtksE1uP793osMAh40MyS8NUYv+M95R2gstf+IH+ulikiuaASCxERkXzIOfckvkG2/rbiW/79+L4H+XPwrYicIZ1BFhERERHxowRZRERERMSPEmQRERERET8nTZDNbJyZpZrZBr+2c81snrcW/Dxvvka81bhe8daCX2dmzfye09frv8XM+gZ6LxERERGRUDuVM8jvAl2Pa3sUWOCtBb+AP0fLdgPqen9xwBjwJdT4Bhq0wDe44MmjSbWIiIiISH5y0gTZObeY7JON+6/5fvxa8O85n+X4JjSvDnQB5jnnfnPO7QLmkT3pFhEREREJudzWIFdzzqUAeLdVvfasteA9R9eJz6k9GzOLM7NVZrYqLS0tl+GJiIiIiOROXs+DnNNa8Ke0RjxonfjC7FSW19USvCIiIhJquT2D/KtXOoF3m+q1H10L/qij68Tn1C4iIiIikq/kNkH2X/P9+LXg+3izWbQEdnslGHOBzmZWyRuc19lrExERERHJV05aYmFmk4COQISZJeObjWIE8KGZ9Qd+5M/lLWcB3YEkYD9wB4Bz7jczexpY6fV7yjl3/MA/EREREZGQO2mC7JzrlcOm6AB9HXBPDq8zDhh3WtGJiIiIiASZVtITEREREfGjBFlERERExE9eT/MmIiJ5LND0h9+PuCYEkYiIFA06gyxShJjZA2a20cw2mNkkMytlZrXNbIWZbTGzyWZWwutb0nuc5G2vFdroRUREgkMJskgRYWY1gPuASOdcQyAMuAUYCbzonKsL7AL6e0/pD+xyztUBXvT6iYiIFHpKkEWKlnCgtJmFA2WAFOAvwBRv+3gg1rsf4z3G2x5tZoFWxRQRESlUlCCLFBHOuZ+A5/HNXZ4C7AZWA7875zK8bslADe9+DWC799wMr3/l41/XzOLMbJWZrUpLSzu7H0JERCQIlCCLFBHeKpYxQG3gfKAs0C1AV3f0KSfY9meDc2Odc5HOucgqVarkVbgiIiIho1kspFAJNNr/ZIrQbABXAducc2kAZjYVaA1UNLNw7yxxTeBnr38ycAGQ7JVkVAC0AqaIiBR6OoMsUnT8CLQ0szJeLXE08A2wELjR69MXmO7dn+E9xtv+hbdapoiISKGmBFmkiHDOrcA32C4RWI/v+z8WGAQ8aGZJ+GqM3/Ge8g5Q2Wt/EHg06EGLiIiEgEosRIoQ59yTwJPHNW8FogL0PQj8NRhxiYiI5Cc6gywiIpIPmVlFM5tiZt+a2SYza2Vm55rZPG9hn3ne4FvM5xVvYZ91ZtYs1PGLFGRKkEVERPKnl4E5zrl6QGNgE75SpwXewj4L+LP0qRtQ1/uLA8YEP1yRwkMJsoiISD5jZucA7fHGBDjn0p1zv3PsAj7HL+zznvNZjm92mupBDluk0DijBNnMHjCzjWa2wcwmmVkpM6ttZiu8yz+TzayE17ek9zjJ214rLz6AiIhIIXQxkAb8x8zWmNnbZlYWqOacSwHwbqt6/bMW9vH4L/qTRQv7iJyaXCfIZlYDuA+IdM41BMKAW4CRwIve5Z9dQH/vKf2BXc65OsCLXj8RERHJLhxoBoxxzjUF9nHimWS0sI9IHjrTEotwoLS3iEAZfMvX/gXfVFKQ/fLP0ctCU4Boby5WEREROVYykOxNzwi+fzebAb8eLZ3wblP9+l/g93z/RX9E5DTlOkF2zv0EPI9v8YEUYDewGvjdW5ELjr3Ek3X5x9u+G9+cqyIiIuLHOfcLsN3MLvOaji7s47+Az/EL+/TxZrNoCew+WoohIqcv1/Mge1PLxAC1gd+Bj/CNoj3e0Us8p3T5x8zi8I3A5cILL8xteCIiIgXdvcAEbyzPVuAOfCe2PjSz/vhOUB2dq3wW0B1IAvZ7fUUkl85koZCrgG3OuTQAM5sKtMY3cjbcO0vsf4nn6OWfZK8kowLw2/Ev6pwbi291LyIjI7WsrYiIFEnOubVAZIBN0QH6OuCesx6USBFxJjXIPwItzayMV0t89PLPQuBGr8/xl3+OXha6EfjC+0KLiIiIiOQbZ1KDvALfoIFEYL33WmOBQcCDZpaEr8b4He8p7wCVvfYHOfFoXBERERGRkDiTEgucc08CTx7XvBWICtD3IH/WSomIiIiI5EtaSU9ERERExM8ZnUEWERERyY1aj34W6hBEcqQzyCIiIiIifpQgi4iIiIj4UYIsIiIiIuJHCbKIiIiIiB8lyCJFiJlVNLMpZvatmW0ys1Zmdq6ZzTOzLd5tJa+vmdkrZpZkZuvMrFmo4xcREQkGJcgiRcvLwBznXD2gMbAJ36I9C5xzdYEF/LmITzegrvcXB4wJfrgiIiLBpwRZpIgws3OA9nirWzrn0p1zvwMxwHiv23gg1rsfA7znfJYDFc2sepDDFhERCTolyCJFx8VAGvAfM1tjZm+bWVmgmnMuBcC7rer1rwFs93t+std2DDOLM7NVZrYqLS3t7H4CERGRIFCCLFJ0hAPNgDHOuab8f3v3H2NZWR5w/Pt0F6SNAgprS9jFxYBWaqzQCW5L01CQhi6ENSk0WCir2Zb4MxhsEGpibJu20CZircR2AdO1xYqikS1iGgU2psZdBVlR2CrblcgGym4FF1qDlfL0j/MOHGbv7pyZe8859975fpLJnB/vzPu89973zDPnnPe88D88fzvFIDFgW+63IXNjZs5k5syKFStGE6kkST0yQZaWjt3A7szcVtZvoUqYH5u9daJ831Mrv6r28yuBRzqKVZKk3pggS0tEZv4n8HBEvLpsOhN4ANgMrC/b1gO3luXNwCXlaRZrgH2zt2JIkjTNlvcdgKR4EH4iAAAPE0lEQVROvRu4KSIOBXYBb6X6R/nTEbEB+AFwQSl7O7AW2An8uJSVJGnqmSBLS0hmbgdmBuw6c0DZBN7ZelCSJI0Zb7GQJEmSaoZKkJ2VS5IkSdNm2DPIzsolSZKkqbLoBNlZuSRJkjSNhjmD7KxckiRJmjrDJMjOyiVJkqSpM0yC7KxckiRJmjqLTpCdlUuSpHZFxLJyG+NtZf34iNhWnhR1c5n0h4h4UVnfWfav7jNuadIN+xSL2Vm57gNeD/wFcDVwVkQ8CJxV1qGalWsX1axc1wPvGLJuSZKm3WVUT4iadQ1wbXlS1BPAhrJ9A/BEZp4AXFvKSVqkoWbSc1YuSZLaERErgXOAPwcuj4gAzgB+rxTZBHyQ6rGp68oyVLc8fjQiovztlbRAzqQnSdJ4+jBwBfBsWT8K+FFmPlPW60+Deu5JUWX/vlL+BXxSlNSMCbIkSWMmIs4F9mTmPfXNA4pmg33Pb/BJUVIjQ91iIUmSWnEacF5ErAUOAw6nOqN8ZEQsL2eJ60+Dmn1S1O6IWA4cATzefdjSdPAMsiRJYyYzr8rMlZm5GrgQuDMzLwLuAs4vxeY+KWr2CVLnl/LefywtkgmyJEmT431UA/Z2Ut1jfGPZfiNwVNl+OQefuEvSPLzFQpKkMZaZW4AtZXkXcOqAMk8DF3QamDTFTJAlqUWrr/xC3yFIkhbIWywkSZKkGhNkSZIkqcYEWVpCImJZRNwbEbeV9eMjYltEPBgRN0fEoWX7i8r6zrJ/dZ9xS5LUJRNkaWm5DNhRW78GuDYzTwSeADaU7RuAJzLzBODaUk6SpCXBBFlaIiJiJXAOcENZD+AM4JZSZBPwprK8rqxT9p9ZykuSNPVMkKWl48PAFcCzZf0o4EdlRi6oZuI6tiwfCzwMUPbvK+X3ExGXRsTdEXH33r1724pdkqTOmCBLS0BEnAvsycx76psHFM0G+164MXNjZs5k5syKFSuGjFSSXmj1lV/wcYnqnM9BlpaG04DzImItcBhwONUZ5SMjYnk5S7wSeKSU3w2sAnZHxHLgCODx7sOWJKl7Q59BdlS8NP4y86rMXJmZq4ELgTsz8yLgLuD8Umw9cGtZ3lzWKfvvzMyBZ5AlSZo2o7jFwlHx0uR6H3B5ROykusf4xrL9RuCosv1y4Mqe4pMkqXNDJciOipcmT2Zuycxzy/KuzDw1M0/IzAsy8ydl+9Nl/YSyf1e/UUuS1J1hzyCPfFS8I+IlSZLUp0UP0quPio+I02c3Dyi6oFHxmbkR2AgwMzPjPY9q3UJHRz909TktRSJJksbBME+xcFS8JEmSps6iE+TMvAq4CqCcQf6jzLwoIj5DNer9UwweFf81HBUvSUM50JWPNxz/so4jkaTp08ZEIY6KlyRJ0sQayUQhmbkF2FKWdwGnDijzNHDBKOqTJEmS2uJU05IkSVKNU01LkqTOLPTJQVIfPIMsSZIk1ZggS5IkSTUmyJIkSVKNCbIkSZJUY4IsSdKYiYhVEXFXROyIiPsj4rKy/WUR8aWIeLB8f2nZHhHxkYjYGRH3RcQp/bZAmmwmyJIkjZ9ngPdm5muANcA7I+Ikqkm27sjME4E7eH7Srd8GTixflwIf6z5kaXqYIEuSNGYy89HM/GZZfgrYARwLrAM2lWKbgDeV5XXAJ7KyFTgyIo7pOGxpapggS5I0xiJiNXAysA34+cx8FKokGnh5KXYs8HDtx3aXbXN/16URcXdE3L137942w5YmmgmyJEljKiJeDHwWeE9mPnmwogO25X4bMjdm5kxmzqxYsWJUYUpTxwRZkqQxFBGHUCXHN2Xm58rmx2ZvnSjf95Ttu4FVtR9fCTzSVazStDFBlpYIR8VLkyMiArgR2JGZH6rt2gysL8vrgVtr2y8p/XYNsG/2VgxJC2eCLC0djoqXJsdpwO8DZ0TE9vK1FrgaOCsiHgTOKusAtwO7gJ3A9cA7eohZmhrL+w5Ak2v1lV/oOwQtQDmbNDu456mIqI+KP70U2wRsAd5HbVQ8sDUijoyIYzwrJbUvM/+NwfcVA5w5oHwC72w1KGkJWfQZZC/XSpPLUfGSJB3YMLdYeLlWmkCOipck6eAWnSD7EHNp8jgqXpKk+Y1kkN4oL9dKaoej4iVJamboQXpzL9dWf4MHFx2wbb/LtRFxKdUtGBx33HHDhifpebOj4r8dEdvLtj+mGgX/6YjYAPwAuKDsux1YSzUq/sfAW7sNV5KkfgyVIB/scm1mPrqYy7WZuRHYCDAzM7NfAi1pcRwVL0lSM8M8xcLLtZIkSZo6w5xB9nKtJEmSps6iE2Qv10qSJGkaOdW0JEmSVONU05I0Ak69LrWr3sceuvqcHiPRUuAZZEmSJKnGBFmSJEmqMUGWJEmSakyQJUmSpBoTZEmSJKnGBFmSJEmq8TFv0gIt5nFePpJIXdn2/cf3+4z6+ZOkhfEMsiRJklRjgixJkiTVmCBLkiRJNSbIkiRJUo0JsiRJklTjUywkSVKrFvP0H6lPnkGWJEmSajo/gxwRZwN/AywDbsjMq7uOQerapJ49sb8ONqnvp6ab/VUanU4T5IhYBlwHnAXsBr4REZsz84Eu49D+/IOvueyv0uQY1/7a1t+W2d/rJDhqS9dnkE8FdmbmLoCI+BSwDvAPrjR+lnx/nZZ/HA/UDpOLqbLk+6s0Sl0nyMcCD9fWdwNvqBeIiEuBS8vqTyLiOx3FNtfRwH9Zt3V34NU91TufefsrjFWfHUaf7/8whoo7rhlhJAs3qa+5/bVdC/pcdPQZHsfPqjE1t6g+23WCHAO25QtWMjcCGwEi4u7MnOkisLms27q7rLuPehuYt7/C+PTZYRh39yY1dvtru4ypGWNqbrF9tuunWOwGVtXWVwKPdByDpGbsr9LksL9KI9R1gvwN4MSIOD4iDgUuBDZ3HIOkZuyv0uSwv0oj1OktFpn5TES8C/hXqsfQfDwz7z/Ij2zsJjLrtu4lW/cBLaK/wpi2pQHj7t6kxj6WcU9RfzWmZoypuUXFFZn73aIkSZIkLVnOpCdJkiTVmCBLkiRJNWORIEfExyNiz4GexxiVj0TEzoi4LyJO6aje0yNiX0RsL18fGEW95Xevioi7ImJHRNwfEZcNKNNWu5vU3UrbI+KwiPh6RHyr1P0nA8q8KCJuLu3eFhGrO6z7LRGxt9buPxhF3eV3L4uIeyPitgH7WmlzWyLi7Ij4bon3ygH7x7I9DeJu7f0fRl/HyGH1eYwdRp/H5zaMY39tENPlEfFAeW3viIhX9B1Trdz5EZER0fojzZrEFBG/W16r+yPik33HFBHHlf5zb3n/1nYQ0+iPkZnZ+xfwG8ApwHcOsH8t8EWq5zyuAbZ1VO/pwG0ttfkY4JSy/BLge8BJHbW7Sd2ttL205cVl+RBgG7BmTpl3AH9Xli8Ebu6w7rcAH23pPb8c+OSg17WtNrfUjmXAfwCvBA4FvjXg8zN27WkYd2vv/5Cx93KM7CDu1o6xQ8bd2/G5hbaMXX9tGNNvAj9Xlt8+DjHVPg9fAbYCM33HBJwI3Au8tKy/fAxi2gi8vSyfBDzUZkylnpEfI8fiDHJmfgV4/CBF1gGfyMpW4MiIOKaDeluTmY9m5jfL8lPADqqZkOraaneTultR2vLfZfWQ8jV3pOg6YFNZvgU4MyIGPQS/jbpbERErgXOAGw5QpJU2t+S5KW0z83+B2Slt68axPU3iHkt9HSOH1ecxdhh9Hp9bMI79dd6YMvOuzPxxWd1K9VznNjU9PvwZ8FfA0y3H0zSmPwSuy8wnADJzzxjElMDhZfkIOngedxvHyLFIkBsYNIVmJwkd8KtRXZL/YkT8UhsVlMtZJ1Od0axrvd0HqRtaantUtxpsB/YAX8rMA7Y7M58B9gFHdVQ3wO+USzC3RMSqAfsX48PAFcCzB9jfWptb0ORzOY7tadqf2nj/29bnMXJYrR9jh9Hn8XlExrG/LvS120B19q9N88YUEScDqzJzv9vk+ooJeBXwqoj4akRsjYizxyCmDwIXR8Ru4Hbg3S3H1MSC++ukJMiNptBswTeBV2TmLwN/C3x+1BVExIuBzwLvycwn5+4e8CMja/c8dbfW9sz8v8x8PdUZgVMj4rVzQxv0Yx3V/S/A6sx8HfBlnj+rsmgRcS6wJzPvOVixQeEOW3dLmsQ6ju1pEtPI3/+OjOPr3UTrx9hh9Hl8HqFx7K+N64uIi4EZ4K9bjAfmiSkifga4Fnhvy3HUNXmdllPdZnE68Gbghog4sueY3gz8Q2aupLq14R/L69enBX/G+w64qV6m0MzMJ2cvyWfm7cAhEXH0qH5/RBxCdfC9KTM/N6BIa+2er+62215+74+ALcDc/3ifa3dELKe6RDPSy7QHqjszf5iZPymr1wO/MoLqTgPOi4iHqC5HnRER/zSnTOttHqEmn8txbM+8cbf0/ndhIqcZ7uI4s1h9Hp9HbBz7a6PXLiLeCLwfOK/WL/uK6SXAa4Et5Vi+Btjc8kC9pu/drZn508z8PvBdqoS5z5g2AJ8GyMyvAYcBfffrBffXSUmQNwOXlFGIa4B9mflo25VGxC/M3ocVEadSvV4/HNHvDuBGYEdmfugAxVppd5O622p7RKyY/e82In4WeCPw73OKbQbWl+XzgTuz3GXfdt1z7kk6j+rew6Fk5lWZuTIzV1MNgLkzMy+eU6yVNrekyZS249ieeeNu4/3vSC/HyGG1eYwdRp/H5xaMY39t0hdPBv6eKjlu+77aeWPKzH2ZeXRmri7H8q0ltrv7iqn4PNWARso/l68CdvUc0w+AM0tMr6FKkPe2GFMTC++v2fLIwiZfwD8DjwI/pcryNwBvA95W9gdwHdXIyW8zopGjDep9F3A/1SjNrcCvjbDNv051ev8+YHv5WttRu5vU3UrbgddRjbi9D/gO8IGy/U+pDjZQdabPADuBrwOv7LDuv6y1+y7gF0f8WT+dMmq/iza39VU+L98rn833T0p7GsTd6vs/RNy9HCM7iLu1Y+yQcfd2fG6pPWPXXxvE9GXgsdrrv7nvmOaU3dLFe97gdQrgQ8AD5XN44RjEdBLw1dKvtwO/1UFMIz9GOtW0JEmSVDMpt1hIkiRJnTBBliRJkmpMkCVJkqQaE2RJkiSpxgRZkiRJqjFBliRJkmpMkCVJkqSa/wdo8+EHDCYf6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(10, 6))\n",
    "subplot(211)\n",
    "plot(percentile(trace[xyh][..., 0], [2.5, 97.5], axis=0).T, 'k', label='$\\hat{x}_{95\\%}(t)$')\n",
    "plot(xs, 'r', label='$x(t)$')\n",
    "legend(loc=0)\n",
    "subplot(234), hist(trace['τh']), axvline(τ), xlim([1.0, 4.0]), title('τ')\n",
    "subplot(235), hist(trace['ah']), axvline(a), xlim([0, 2.0]), title('a')\n",
    "subplot(236), hist(trace['mh']), axvline(m), xlim([0, 1]), title('m')\n",
    "tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Again, we can perform a posterior predictive check, that our data are likely given the fit model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/4000 [00:00<?, ?it/s]INFO (theano.gof.compilelock): Refreshing lock /Users/twiecki/.theano/compiledir_Darwin-18.5.0-x86_64-i386-64bit-i386-3.6.7-64/lock_dir/lock\n",
      "100%|██████████| 4000/4000 [00:05<00:00, 712.25it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c2627f668>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate trace from posterior\n",
    "ppc_trace = pm.sample_posterior_predictive(trace, model=model)\n",
    "\n",
    "# plot with data\n",
    "figure(figsize=(10, 3))\n",
    "plot(percentile(ppc_trace['zh'], [2.5, 97.5], axis=0).T, 'k', label=r'$z_{95\\% PP}(t)$')\n",
    "plot(zs, 'r', label='$z(t)$')\n",
    "legend()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
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